Axle differential problems

When I took my Valiant in for repair, I asked to see if they could diagnose a bumping sound in the back of the car. The mechanic showed me that the axle moved too freely. My question is; Is it safe to drive with an axle differential problem? I guessing that if that is the problem, I am looking at a costly repair and may have to wait to get the money for it. Thanks in advance for all your help.