I think a bigger question is what will they do for that long?

All the things like stars will be long gone and dead before that time leaving us with long lived black holes and radiation. So everything would be based on virtual world can computation by that point. Do you just cool everything to near absolute zero and run it as slow as possible to you can last as long as possible?

The History of the Universe channel has an episode around this, but I'll have to figure out which one it was.