I cam across this article that says the leaves could be saved if cut and set in a glass of water like in this article. Is this true? Can I propagate hostas this way? https://www.hometalk.com/3899783/you-can-save-that-hosta
Looks like your hosta is in too much sun and/or is not being watered enough. It seems to be one of the blue-leaved hostas, and these hostas are not known to be particularly sun tolerant (the gold-leaves ones can take much more sun than the blue-leaved cultivars).
If your hosta is indeed in the shade (about 4 hours or less of sun), then I wouldn't worry about it - just make sure it's getting enough water. If it's NOT in the shade, then the easiest way to save it is to transplant it to a location that IS in the shade.
Your link shows someone saving leaves that have a bit of the crown attached, which looks doable, but then again, the author of that page confuses moles with voles, so...