I think it would be one of 3 reasons for this:
1) Their spirits are released from their body (Abe's little glowing things/birds) So the body is useless without a soul and shrivels up since the soul was the only thing making it stay alive.
2) Maybe on Oddworld you rot extra fast. (So you'd have to eat those fruits & veggies fast!
)
3) The programmers just did it so there would'nt be a bunch of dead sligs lying around everywhere you go.