That's actually a yes/no answer type of question. I know, I know, that's cryptic... just like everything else "morel". LOL
IF you hunt dying Elm like I do, that particular tree may fruit up morels, and it may not. I'd say that oh, 1 in 15-20 dying Elm I check may have morels. Now, once that same Elm is completely dead, forget it. Don't even check it.... no morels. That's when you'll see the Pheasant-backs on the dead trunks.
NOW. If you hunt living trees, such as Poplar, Ash, even old Apple, then you are more likely to find morels year after year in those settings.