People posting content on social media should be held accountable when what they post is knowingly false. If someone hurts the reputation of another on social media, the victim should be able to take legal recourse to remedy the situation. This would hold social media users accountable for the content posted on their pages.
There are many sites and hoax posters that claim a celebrity is dead all the time. They do it for attention or just to ruffle some feathers. No one ever actually gets sued because people can find out pretty quickly if it is true or not. Claiming someone is dead is not necessarily libel either.
It seems like once a week or so there's some online hubbub about a celebrity being dead that isn't true. There should certainly be no criminal charges for people who spread fake rumors, because they aren't bound by anything NOT to spread fake rumors. It's not like these guys are in the press and have an ethical obligation to make sure what they say is the truth.
Seems it would be very hard to prove that the Facebook post somehow damaged Stallone's reputation, which is a key element of a libel lawsuit. If it was shown to be damaging somehow, then yes Stallone would have the right to sue. Not sure what he'd hope to gain from it though, just by being alive he's already proved it was nonsense.