When I was at school participating in a legal clinic I had lots of clients facing eviction and we had plenty of tricks to use. Most popular was to demand a jury trial, which could take a month or two to organize, during which time the tenant wasn't paying rent and so could save enough to move. The basic procedure: http://www.courts.ca.gov/27723.htm
Kind of shocked to hear about this happening at a "legal clinic". I'm familiar with the business structure behind these types of programs and they're invariably seedy characters involved with a paralegal group and lots of cold calling. Clogging up the courts so you can avoid paying rent... shrug
As for seedy, this isn't ambulance chasing. This is law students helping the poorest of the poor. Nobody ever cold calls anyone (Where did you see that?). There is no profit to be had. Most legal clinics are funded by law schools and similar institutions. And I say "funded" as in they give them a place to meet clients. Our clinic moved around, seeing people in church basements and community centres after hours. The licensed lawyers we worked with all acted pro bono. This is poor people being treated very badly and needing the help of lawyers they cannot afford.