Can an employer ask me to sign a non compete document after I have been terminated?

I recently was hired by a company (hourly not salaried) and was sent to several days of training out of state. Airfare and hotel bills were paid by the owner, and I expensed the food and the ground transportation costs (car rental). I was to be paid a reduced rate during training hours. We did not discuss pay during travel time before I went to training, but I expected something and intended to discuss it with the owner upon my return. Upon return from training, the owner decided to terminate my employment and handed me a termination letter. Subsequent to that, the owner asked that I return my equipment (laptop, scanner) and for me to complete documents, provide copies of specific identification documents. I complied with this request. He then asked me to sign a non-compete agreement several days after the termination letter was given to me. Do I need to sign this document in order to receive payment for both my expenses and time for having attended the training? Why would I be required to sign a non-compete when I had already been terminated? Is that enforceable? If the company doesn't reimburse me, do I have a legitimate case to pursue?