What does Eddie do when Venom eats?

Well, in the actual comics there was one point where the symbiote wanted to consume human flesh but Eddie was able to get rid of its cravings by eating chocolate. It is kind of funny though because well before this story Venom would tell some enemy of his that he'd eat some organ/body part of theirs but then he would never actually do it.

LET THE BIG DOG EAT THAT DOG WILL HUNT!

At the end in Mrs. Chen’s shop, it did look like Eddie was “kinda” swallowing what Venom ate. And in the scene where She-Venom saves Eddie... Anne is horrified by the fact that she, Anne, bit off a guy’s head. Eddie’s reponse to that? “... I’ve been there, too. It’s not fun!”

We know it was really Venom who did this but maybe Eddie does digest Venom’s... leftovers. :D Whether this deviates from the comics or not is irrelevant.

Given how fast Venom can regenerate Eddie's body, plus the scientists discovering how Symbiotes were consuming internal organs of their hosts (because they weren't fed proper live stock) I believe that they can and will digest anything almost instantenously. Also, in the movie, it is very clear that it's not just a suit, because it definitely survives inside the hosts body, modifying it (or destroying it) as they see fit.

Venom is not a suit, it merges with the body and thus anything Eddie or Venim eats - both do.

The symbiote integrates itself into the host's physiology. It's not just a suit that's worn on the outside.