Sort of. The term comes from Greek. In aristocratic Greek culture, men held nightly parties called symposia that involved dinner followed by drinking and conversation/entertainment. Greek culture thrived on reciprocity. It was understood that if you were invited to one of these parties, you would return the favor by hosting or by contributing food, drink, etc. The parasite was the person who ignores these reciprocal obligations and goes to one of these dinner parties without the ability or intention to pay it back.

The parasite is a stock figure in comedy (eg Khremon in Aristophanes' Wasps), the man who lurks outside of bathhouses waiting to ambush honorable aristocrats to get a dinner invitation. He is often portrayed as gluttonous, lustful, shameless, lazy and a drunkard. A freeman who is willing to play the role of a slave (by running errands, acting as a go-between, etc) in order to get food.

There are some who debate the reality and the extent of this trope. It fits very neatly into Greek ideas that aristocrats are innately better than the poor who are sneaky, sniveling, and driven by carnal desires. I think you could find parallels in almost any other system with arbitrary drastic inequalities where literary tropes serve to validate the system of power. And while there might be some truth to it or some cases of life imitating art, it seems to be far more prevalent as a trope than a reality.

This trope was pretty much copied straight into Roman comedy and satire (Roman comedy is pretty close to being straight translation of Greek New Comedy). However, it's unclear about the reality in the Roman context. Romans had a very different system of social hierarchy, part of which involved aristocrats (patrons) providing meals for the less fortunate (clients) in exchange for political support, etc.