If a work permit expires, can I work while my residency is processed?

You must inform you with a trained person or at the immigration offices so as not to commit a violation that affects you

No. You should have requested a new permit three months in advance and it would have arrived. Anyway, call immigration or connect to the www page. uscis .gov.y check because many things have changed. Be careful if he says no. because you can lose the right to residency if they catch you.