They must have had a primitive version of tanneries.
There would have to be a secure space where the bones and a hides could dry out, without any hungry animals trying to eat or chew them. The aroma of new blood and freshly torn flesh would advertise the location of that secure space.
Maybe there was a form of Cave Man sentry posted. Someone standing by with a pile of rocks to throw at any approaching beast.
Any encroaching critter would just go onto the menu, or become a nice fur coat. It wouldn't surprise me to learn that they invented leatherworking, and all subsequent leatherworking has just been passed down.
There would have to be a secure space
There’s a name for any hungry animals trying to take a Neanderthal’s kill from their caves:
Dinner.
Even cave bears, cave lions and cave hyenas beat tracks when the Neanderthals claimed a cave.