When applying brakes and as the car slows down a loud thumping noise can be heard from the rear wheel until the car completely stops. When letting the car coast to a stop and gently applying the brakes the noise cannot be heard or is greatly reduced. No noise can be heard while driving normally.

Any ideas what this might be? Thanks.

I would say that you either have a bad strut or your rear drum brake is warped. I would guess it's th strut though.

I also had this problem, and no mechanic was able to recreate the sound / diagnose it. On an unrelated note, when getting oil changed (not my regular mechanic) they "noticed" my rear drums needed to be resurfaced. Never did mention the thumping sound to them -- just using them because of coupon. Had my regular mechanic look at drums and said yes they need work. After having that fixed, the sound went away.:iceslolan