Passive clauses without auxiliaries

In both of your sentences, what you have is the passive participle typed, which syntactically functions as a noun modifier. When typed is being used alone, it follows the normal rules for modifier placement and precedes the noun:

I found a typed letter.

However, as a passive participle typed is able to take an adverbial complement that specifies the agent. When this occurs, the entire phrase must then follow the noun.

I found a letter typed by the secretary.

This rule is not unique to passive participles: in general, English requires single-word modifiers to precede a noun, but multi-word modifiers to follow the noun. (The exact rules are fairly complex, but the preceding rule of thumb covers the most common cases.) You can see the same thing with active participles ending in -ing and ordinary adjectives.

I saw a red ball.

I saw a ball red as the rising sun.

I met a dying man.

I met a man dying of AIDS.

I don't have a copy of the CGEL to refer to, but if you look up the section on adjective and adjective phrases I'm sure you'll find a discussion of adjectival word order.

Note that this pattern also exists for the verb to be: the man who is tall becomes the tall man whereas the man who is in the room becomes the man in the room.

I think the answer to your question lies in the rules for adjectives which follow the nouns that they modify. These reduced adjective clauses are, for all purposes, adjectives themselves and when they are reduced to a single word, they are positioned as a normal adjective, that is before the noun. However they follow the noun when they have more than one word after being reduced, just as with other multiple word adjectives in English (except hyphenated adjectives).

For example, you can't say He has a black as the night soul but you can say He has a soul black as the night. The adjective phrase black as the night follows the noun soul because it is a phrase not a single word.

You can't simply say, *I came across a letter typed,

This is not so.

“As I went through his correspondence, the letters were all handwritten until I came across a letter typed.” Here, typed is a depictive adjective. The sentence equates to “I came across a letter and it was typed.”

In I came across a typed letter, from the syntax, typed* is clearly functioning as an adjective.

It is the distinction between adjective and verb that has to be maintained in order to express an idea clearly.

In I came across a letter [that was] typed by her secretary, compared to *I came across a letter typed.” you will notice two things:

1 The lack of an agent in the latter.

2 Except for the depictive reading, the natural reading of the latter goes to understanding of “typed” as a postpositional common adjective but, because of standard syntax, it is non-standard/not idiomatic here.

With the disappearance of clear grammatical cases, syntax took on a crucial role in English.

In I came across a letter [that was] typed by her secretary, typed must be understood as a past participle – a verb. This can be done by

3 including “that was” and/or

4. including “by her secretary”, which is adverbial. However this is not essential to the understanding, as adverbs may qualify verbs or adjectives, but it does not hinder the understanding of "typed" as a verb as the listener reader will recognise a passive.

Now consider

I came across the number of species that were seen/recorded by the members.

I came across the number of species seen/recorded by the members.

I came across the number of species seen/recorded.

I came across the number of seen/recorded species.

The reason Huddleston and Pullum don’t discuss it is perhaps that it is as at least as much a semantic question as a grammatical one. Typing is a process and, as such, not something you just come across. Moreover, a mundane process such as typing is not one you would normally want to comment on unless you wanted to draw attention to the fact that it was typed by her secretary, or typed that morning or typed in red ink. By contrast, it would be quite reasonable to say I have seen a jet engine assembled because that is something you see rather than come across, and it is sufficiently out of the ordinary to report for its own sake.