Don't pay until they sue you

1. Can They Collect from you?

 

This is the only legal basis they can rely on: http://en.wikipedia.org/wiki/Filial_responsibility_laws Depend on the states, laws are different. Usually they don't sue for mere $500, but they could.

 

2. Does this impact GC?

 

No impact on green card. This is private debt, not public welfare. Your mother doesn't have to pay, if she doesn't care about her credit history. see http://www.uscis.gov/green-card/green-card-processes-and-procedures/public-charge