Some play may be alright. Assuming a Track/Kick? There is a seal at the end of the differential housing where the axle shaft goes into it. Any signs of leakage at all? You may want to pull the fill plug and check for the fluid level. It may not be leaking because it is empty. If it has fluid, and no leak, roll with it!
The axle is splined and fits into splines inside the differential. There is a C clip at the end of the splined shaft that holds it in place.