Living weapon is an interesting card, putting creatures in a place they usually don't go. I've tested (and am still testing) whatever strange interactions it occurs to me that this might cause. So let's find out what happens when you endow a crusader with a crusader's ability to endow, whether an infected dies while being a weapon, and what on earth ferro golem is supposed to do to itself in the weapon slot.
The first general rule that seems to stay consistent is that a creature that becomes a weapon remembers what its its hp stat was, but doesn't change it. This means a living weapon can't die by normal means, whether CC (which won't target it), poison that it had before becoming a LW, or other delayed changes to its hp. This applies to hp increases as well. Other status effects also seem seen carry over. With that in mind, here's a list of specific interactions.
Note: The following list of interactions is incomplete. Feel free to suggest additional experiments, or conduct them yourself!
Sorry if you were looking for more, it's annoying to do this on mobile so it'll be up in more detail later.