hi and welcome.

how big was the plastic piece was? do you know? if the clump of plastic not bigger than a tennis ball, sometimes your cat would be lucky, having it come out by his "rear".

are you sure about "hard" tummy? cats often have that after they don't bath themselves, for the cases of stomatitis and heartworm mostly. but heartworm wouldn't cause yellow "bile". did you check your tuna's mouth too?

otherwise, if those questions are too much for you...take him to vet just to be sure! good luck.