TL;DR: My leopard gecko has a dead toe from stuck shed. Thought it would fall off at some point, but it's been weeks and it hasn't. What do?
I adopted a leo approximately 5 weeks ago, from a friend who bought a pretty morph at an expo without any prior intention or planning. They've taken decent care of her but I'm still dealing with a couple of knock-on effects regarding their health and habitation that I'm looking to improve. Most notably: they didn't appear to be good at removing stuck shed from toes. And unfortunately, since I am a new keeper, I didn't identify it as stuck shed at first, and it was left unremoved for about a week (plus however long it was stuck with the prior owner). One of her front toe-tips constricted and has since remained very grey-and-white, even after I emergency-bathed her and removed the shed with cotton swabs. I am completely certain that it is dead. It's been a few weeks since this has happened, and I was under the impression that it would at some point fall off, but I'm wondering if I'm mistaken in that. All the online guides focus more on preventing this than dealing with it, so it's hard to know where to go from here. Advice?
For the worried parties, don't worry, she has since successfully shed in my care, and I was proactive in searching for (and have successfully removed) stuck shed since.