meaning of "running cases", "hang around hospitals", "get a cut"

[kjc0123]

What is the meaning of "running cases", "hang around hospitals", "get a cut" in the following sentences?

 

I'm running cases for some local ambulance chasers, a bunch of sleazy ******** who advertise on cable and hang around hospitals. I sign 'em up and get a cut.

[Ouisch]

An ambulance chaser is a low-class lawyer (or attorney) who makes his money by literally following ambulances to hospitals in hopes of getting the patient as a client (in case the patient was involved in an accident and wants to sue).  It sounds like the man "running cases" in your example waits around in hospital corridors, listening to the conversation between doctors and nurses in the hallways and locates patients who are accident victims that might be interested in a lawsuit.  When he finds such a patient, he puts them in touch with one of those ambulance-chasing lawyers, and, in turn, he receives a portion of the attorney's fee for his referral.