I would think that maybe they would finally cremate him, and display his urn and a death mask. Kind of Abraham Lincoln-esqe. As I understood it, Stalin wanted Lenin's body preserved so that everyone fully understood that he was dead, and that Stalin was in charge. "Lenin" wouldn't reappear
Barbarosa-like and call him out.
I wouldn't be surprised if they just unceremoniously dumped Stalin's body in a conrete hollow and walled it up.