Can I still buy this house even though I got fired?

My offer on a house just got accepted a month ago. I am in CA and the house is a HUD home. I have just submitted the loan application and was waiting for approval and closing. I was fired from my job of four years today. What is the chance that I will still get the house? Will they check if i still work there? Should I tell the lender? Can I add a co-signer to the loan and still have a chance? I will apply for unemployment. Thank you