[susan53]

Two problems here :

a) There is a subject - which. That's why it is called a pronoun. like other pronouns which/who can act as subject or object of the verb, but does so by joining the two clauses into one sentence, whereas an equivalent pronoun would leave them as two sentences. Compare:

1) I broke my plate, which had been engraved
I broke my plate. It had been engraved. (which/it as subject of the verb)

2) I liked the book which John gave to me.
I liked the book. John gave it to me. (which/it as object of the verb).

With most verbs, the relative pronoun (which/who/that) can only be omitted when the pronoun is the object of the verb and the clause is defining - eg :
I liked the book John gave me

b) Your example is not of a defining relative clause but of a non-defining one. Notice that I've added a comma - if you can do that (and in your example it would be likely) then it's non-defining. If you wanted to make it defining, you'd be more likely to say :
I broke the plate which had been engraved.

c) However, a reduced relative clause is one where both the relative pronoun and the verb BE have been omitted - and here and only here the pronoun can be subject :

The book (which is) on the table needs to go back to the library.
The man (who was) waiting in reception has left.
The book (which had been) left on the table was badly damaged

d) So - to now answer your question - why isn't a) I broke the plate engraved possible but b) I broke the plate engraved at the fete... is ? It follows all the rules above. It seems to me that in (a) engraved functions as an adjective and must therefore pre-modify the verb I broke the engraved plate whereas the addition of the propositional phrase in (b) makes it clear that it is part of a clause and the reduction can therefore take place. Compare :

i) *I need some shoes heavier. /I need some heavier shoes
ii) I need some shoes which are heavier
iii) I need some shoes (which are) heavier than these.

Again - in (i) the adjectival function is predominant and heavier must therefore pre-modify the noun unless there is the explicit addition of a subject and verb (which are). However, in (iii) the use of than these allows a clausal interpretation and the elision is therefore acceptable.