That's awful, Malu
I have no idea if that's standard practice in the US if your supervisor moves institution; here in the UK, you are registered at a university, not tied to a supervisor, and your department would have to find you a new supervisor.
But how can they just fire you as a research assistant? Don't you have a contract? Don't you have a right to proper procedure? There must be a level within the university to which you can appeal. I know my experience is with British universities, but I can't imagine that American ones can be quite that different in terms of fair treatment.
I hope that something works out for you.
Wendy