You have to look at the process that happens when you press the button. If pressing the like button results in a specific set of actions then that can be patented, and apparently was. Pressing the like button causes specific things to happen and that's what was patented, not the button itself which is essentially just an image link.
Patents don't become void simply because the registering party dies, I don't see that aspect of the case as a problem though I'm sure Facebook will argue it anyway.
I'm not a lawyer though and it's obvious that no judge will ever force Facebook to stop allowing people to like things, it would impact too many people. This is a money grab, it will surely be settled out of court.