When you collect unemployment, you have to say you are ready and willing to work and activly seek employment. When you apply for SSDI, you say you can't work. It's a contradiction. I was advised by my social services caseworker to stop drawing unemployment before you apply for SSDI.
I applied for SSDI 1 yr after my accident, which I was receiving unemployment during that 1 yr period. My backpay was approved for that same period (minus the 5 mos., of course) and paying back unemployment hasn't been a issue.