If it's dying, a roach would eat it, including other roaches. While it does make them quite the pest, it also makes baiting and killing off a roach population simpler.
Roaches will feed off organic matter, things like dead or dying plants, dead animals that are decaying, they will even feed off each other. So, if a roach in their community dies, they will all sit around that other roach and have a feast. That's also why Pest Control companies can eliminate a population by using baits that make one sick and die the rest will feed off of it that's how it spreads through a roach community.