I would say no. Lenders want to verify employment and the ability to repay the loan. If you are unemployed and collecting unemployment, how can you guarantee the lender that you will be able to repay the loan when your unemployment benefits run out?
As soon as you land a job, hopefully in the same line of work, you could possibly start the refinance process. Your lender will want to see tax returns, last 2 paystubs, 2 months bank statements, and more. They will also verify employment.
Best wishes find a new job!