leech

(noun) carnivorous or bloodsucking aquatic or terrestrial worms typically having a sucker at each end. Synonyms: bloodsucker, hirudinean.

(noun) a follower who hangs around a host (without benefit to the host) in hope of gain or advantage. Synonyms: parasite, sponge, sponger.

(verb) draw blood. Synonyms: bleed, phlebotomize, phlebotomise. Example: "In the old days, doctors routinely bled patients as part of the treatment."