I beg to differ: I do not believe that any English-speaker would use the participle 'eaten' adjectivally, any more attributively

*An eaten chicken was found in his stomach.

than predicatively.

The meaning you cite could, in my view, be expressed only through its combination with a present perfect VP, thus:

The chicken has been eaten.

, which, of course, is no more than a passive with ellipsis of agent!

N.B. The above objection does not, of course, extend to cases of modified attributive participles, such as a recently eaten chicken (= "a chicken that was recently eaten", i.e. a passive relative clause simply compressed into the form of a premodifying phrase) or of established compound adjectives, such as half-eaten.