Полная таблица того, что может быть в роли того или иного элемента клоза выглядит так:

Сокращаем сложное предложение. Безличные обороты/клозы в роли элементов предложения.

Мы уже рассматривали все возможные сложные формы инфинитива, которые получаются из личных форм путем "обезличивания", т.е. вместо личного глагола (он всегда первый в "цепочке") ставится базовая форма (т.е. фактически инфинитив этого глагола). Например, группа Progressive – 'am inviting', 'was inviting' и т.п. превращается в 'to be inviting' и т.п. Все эти сложные формы могут поначалу показаться безумно сложными, но на самом деле твердо опираются на схему грамматических времен: I write/I am writing – I have written/I have been writing (и плюс пассивы, построенные так же по этой схеме).
Точно по такому же принципу образуются сложные формы причастия.

Simple
I invite → inviting
I am invited → being invited

Progressive
I am inviting → being inviting
I am being invited → being being invited
Слишком много -ing получается в одном месте (а в пассиве аж два being) поэтому эти формы не употребляются.

Perfect Simple
I have invited → having invited
I have been invited → having been invited

Perfect Progressive
I have been inviting → having been inviting
I have been being invited → получится еще хуже, чем было до "обезличивания".

Having been inviting – cлишком сложная форма, хотя где-то раз в сто лет может и встретиться, и таким образом получается четыре формы причастия/герундия (они полностью совпадают) – две активные и две в пассиве:

inviting -- being invited
having invited -- having been invited

В разговорной речи сложные формы причастия почти не употребляются (в основном в журналистике и то не часто), но посмотрим на примеры:

Being asked whether she…= когда ее спросили…
Having lived in London for several years… = прожив в Лондоне несколько лет….
Having been sorted the letters… = после сортировки письма…

А вот сложные формы герундия (по виду идентичные причастиям) употребляются гораздо чаще в том числе и разговорно речи:

She screened her face to avoid being recognized = она прикрыла лицо, чтобы ее не узнали.
So you don't like being rubbed the wrong way! = Aга, не любите, чтобы вас против шёрстки гладили!
They live in hourly dread of being caught = они живут в постоянном страхе, что их вот-вот поймают.

Let's drink to his having returned.
Everyone suspected him of having murdered his rival.
He gave no sign of having heard.
I don't recollect having said that.

I remember having been shown the book = я помню, что мне показывали эту книгу (но эта сложная форма употребляется очень редко).

Общая идея безличных клозов состоит в том, что они заменяют более компактным образом личные клозы. Возьмем два похожих предложения:

The spectators leapt to their feet and roared approval.
The spectators roared approval and leapt to their feet.

Их можно преобразовать в такой вид:

The spectators leapt to their feet, roaring approval.
Roaring approval, the spectators leapt to their feet.
The spectators, roaring approval, leapt to their feet.
Leaping to their feet, the spectators roared approval.
The spectators roared approval, leaping to their feet.
The spectators, leaping to their feet, roared approval.

Такое употребление английских причастий соответствует русским деепричастиям.

Та же идея замены применима и в остальных случаях.

When you are writing a business letter, begin 'Dear Sir'.
When writing a business letter, begin 'Dear Sir'.

After he was in the army, he was an engineer.
After being in the army, he was an engineer.

While I am not optimistic I have not given up all hope.
While not being optimistic I have not given up all hope.

The people who are sitting here in the sun are tourists.
The people sitting here in the sun are tourists.

Will anyone who wants a ticket please apply to me.
Will anyone wanting a ticket please apply to me.

The boys who have shouted/who have been shouting the loudest are the winners.
The boys the loudest are the winners.

The boys who has shouted/who had been shouting/who shouted/who were shouting the loudest were the winners.
The boys shouting the loudest were the winners.

We have sat here in the sun for two hours and are very thirsty
Having sat here in the sun for two hours, we are very thirsty.

В случае -ed participle clause – это обычно сокращение клоза, где глагол в пассивном залоге:

When this house is/has been painted white, it is looks bigger.
Painted white, this house looks bigger.

I like your house if it is/has been painted white.
I like your house painted white.

I will gladly come to your house if/when/whenever I am invited.
I will gladly come to your house if/when/whenever invited.

I won't come until/unless I am invited properly.
I won't come until/unless invited properly.

Although I was invited, I didn't go.
Although invited, I didn't go.

Even if (I am) invited/ Whether I am invited or not I won't go.
Even if (I am) invited/ Whether invited or not I won't go.

I am returning your letter, as I was requested (to do).
I am returning your letter, as requested (to do).

When she was told the party was cancelled, she burst into tears.
On being told the party was cancelled, she burst into tears.

Cars which have been parked illegally will be removed.
Cars parked illegally will be removed.

The castle, which was burnt down in 1485, was never rebuilt.
The castle, burnt down in 1485, was never rebuilt.

We were delayed by heavy trucks which were being loaded onto the ship.
We were delayed by heavy trucks being loaded onto the ship.

Will the students who are interested/concerned/involved please write their names on this piece of paper.
Will the students interested/concerned/involved please write their names on this piece of paper.

I hope that I'll be able to come.
Hope to be able to come.

We consider that he is very trustworthy.
We consider him to be very trustworthy.

We thought it wrong that he should be punished.
We thought it wrong to punish him.

He worked all night so that he could get the job done in time,
He worked all night so as to get the job done in time,

His work was so good that it made him internationally famous.
His work was so good as to make him internationally famous.

He was in such bad health that he was obliged to resign.
He was in such bad health as to be obliged to resign.

I don't know what I should do.
I don't know what to do.

I don t know wno(m) I should ask.
I don t know wno(m) to ask.

Can you tell me where I should go?
Can you tell me where to go?

I wonder when I should leave.
I wonder when to leave.

Tell me how I can start this car.
Tell me how to start this car

I haven't decided whether I shall sell it or not.
I haven't decided whether to sell it or not.

We must reach a decision (as to) whether we should sell.
We must reach a decision (as to) whether to sell.

An infinitive clause can replace relative clauses corresponding to the examples below:

The thing that you should do is what everyone else is doing.
The thing that to do is what everyone else is doing.

The person (whom) you should ask is George Lamb.
The person to ask is George Lamb.

The place where you should go is Brown's.
The place where to go is Brown's.

The time when you should leave is after they've served coffee.
The time to leave is after they've served coffee.

The way you should start it is to give it a push.
The way to start it is to give it a push.

The question of whether we should sell is still undecided.
The question of whether to sell is still undecided.

An infinitive clause can also replace relative clauses in the following types of example:

You need someone who can look after you.
You need someone to look after you.

I've brought a book that I can read.
I've brought a book to read.

George is the man for whom we should vote.
George is the man to vote for.

He was the first man who flew across the Atlantic.
He was the first man to fly across the Atlantic.

Инфинитив может быть в пассиве:

There are several people who have to consulted.
There are several people to be consulted.

There are still many obstacles that must be overcome.
There are still many obstacles to be overcome.

There is a lot of work that must be done first.
There is a lot of work to be done first.

Is he really a man who can be trusted?
Is he really a man to be trusted?

Инфинитивые и -ing клозы по структуре близки к пяти основным типам для личных клозов. Таким образом:

1. We waited.
While waiting, we did our homework.
I have come to apologize.

2. He was my friend.
Being my friend, he helped me a lot.
To be successful, you must never give up.

3. I made a mistake.
Having made that mistake once, I won't make it again.
I am very happy to see you again.

4. I gave him an answer.
Giving you the answer would be cheating.
To tell you the truth, I don't know.

5. I found him a bore.
Finding him a bore, I kept out of his way.
She tries to make everyone happy.

То есть, глагол в безличной форме также может употребляться "само по себе" или иметь комплементы и дополнения.

Делаем описания более подробными и усложняем группы.

Verb phrase = (auxiliary/auxiliaries) + main verb

The ship sank.
The ship is sinking.
The ship has been sunk.
The ship must have been sinking.

Noun phrase = determinative + (premodification) + head + (postmodification/complementation)

I remember him
I remember his wedding
I remember that girl with the red hair
I remember all those days in the country last year.
I remember a better story than that.
I remember the best trip that I ever had.
I remember a good trip that I once had.

Adjective Phrase = (premodification) + head + (postmodification/complementation)

The weather was pleasant.
The weather was pleasant enough.
The weather was incredibly cold.
The weather was too hot to be enjoyable.

Adverb phrase = premodification + head + postmodification/complementation

I spoke to him yesterday.
I spoke to him quite often.
I spoke to him very severely indeed.
I spoke to him as clearly as I could.