Can a car be repossessed from a military base?

It is possible, and very probable considering that it is a violation of military regulations for any service member to dishonorably indebted.

Some repossession agents have special permission to enter military installations from the commanders of those installations for the purposes of repossessing vehicles. In most cases, not that it matters for the answer, the agents must contact the Provost Marshall or MP/SF/SPs and notify them of the vehicle they are recovering; but, this is not always required.