The lien holder signs when they get paid, then after they sign, you are suppose to sign the title also over to them.
I would not give them any POA personally, but that is just me, I would make them bring me the titles to sign personally But if I did give them anything, it would be only a limited POA and for only the signing of the title on that one specific auto.
I am stll of the firm belief that the other persons insurance company will cheat you any chance they can.