Can 吃的人 mean both a person who eats something and a person who someone eats? If a subject or a object is omitted.
In the right context, '吃的人‘ can mean 'the person who we are eating'.
Reminds me of that old joke:
2 cannibals are eating a clown, one says to the other, "Does this clown taste funny to you?"
Very funny in English, not so sure in Chinese， humour does not translate well!
In addition to other answers:
The form "吃的x" is not disambiguated by syntax, but by semantics.
In common sense, a person is not to be eaten, so "吃的人" would only mean "man who eats" (except when there is very explicit context to let it mean otherwise).
On the other side "吃的鱼" would mean "the fish to be eaten".
This is an interesting question.
By default, 吃的人 would mean 吃xxx的人， like 吃肉的人. Example, 这东西吃的人很少 means 吃这东西的人很少.
If you truly want to denote 'a person who someone eats', you could say '所吃的人' or '所吃之人'.
One of usage of 所 is to precede a verb to indicate the following object is the receiver or accepter of that action. In this case, 所吃的人, 吃 is a verb and 人 is the target. So, 所吃的人 clearly denotes 'a person who was eaten'.
Here is some examples:
他所吃的人 // the one who he ate;
你知道他所吃的人是谁吗？ // do you know the person who he ate?
On top of that, if you say 吃的东西(食物)， it would mean 所吃的东西(食物)--something（food） that was eaten. Like, 我们吃的东西==我们所吃的东西==something we eat.