No, if you are fired, it is impossible to claim

unemployment benefits. Posted so many times here, if it is not your errors, and you are not laid off, but fired following steps

1. deny sign any document employer passed to you
2. find a lawyer and open a case immediately
3. as long as the case if not closed, you have rights to continue working get paid
4. infinite loop to go court, until you or your employer getting tired and quit

The key here is never leave the job and continue fighting. If you already gone for the job, there is nothing you can do. Remember here is America, you have to fight for yourself, no other way out.