They will give away what they can to museums who will take what they can (museums are space limited). Most of it will probably go in a dumpster.
Frankly they will probably do a much worse job than whoever miller's heirs would. Private individuals tend tend fall back to give that sort of stuff away to other private collectors when they can't give it to museums. Government agencies don't expend nearly as much kind of effort on that kind of thing nor do they have a workflow for posting free shit ads on enthusiast forums, FB marketplace and CL. They do however, have people who's normal duties involves throwing things in the dumpster, so that's what will happen to it in all likelihood. The stuff that's in cases and ready to display will probably all fine homes but whatever stuff was low value enough that Miller wasn't already displaying it will probably mostly be thrown away.