I've seen a couple minor, older-hardware cases when they've been powered off with something on the screen for years, but that's about it. in theory they can also "burn in" by not clearing the display occasionally (afaict it has something to do with accumulating charge) but most or all of those should clear eventually after cycling a bunch (afaict, though it can definitely persist to a minor degree for dozens of full refresh cycles). extreme ghosting, basically.

they seem pretty durable to me.