Staff will tell you that how you run your wiki is pretty much up to you (so long as you don't violate TOU).
If you don't mind my thoughts: my experience is I will strip inactive Chat Mods, Rollbacks, and Admins, with a note to chat with me if they return. (Wow! You got a Wikia Star here! Kewl beans)
I mainly do this so users in the community will not see the Admin tag and waste time on someone inactive when they need help.
You cannot do anything about bureaucrat as only they themselves and Staff can remove them. (word of warning: if ever exploring your own User Rights pages, be careful to NOT remove your own b'crat!) Since b'crats can re-promote themselves, no probs there. Besides, on most wikis the default setting has the "Bureaucrat" tag unseen.
I generally do not bother with Founders since the tag remains the same even without Admin, and as a matter of courtesy to the person who started the wiki.
In short: demote the inactive Admin, don't worry about the Founder. Or the Wiki Star, who is still active anyway.
I have experienced where it got stuck on one particular former admin and I had to edit it to explicitly be my name. Of course, that particular wiki has the entire administration stripped by Staff before they instilled me in place, so it might have been an issue with that process.
At any rate, that is where you can change it if you wish. @latest is the last admin with activity, which will fall back to a Staff member should all admins go inactive (60 days).
Other options include @sysop, last admin, no fall back to staff; and specific user(without linking).
You can alter a lot of wikia-defaulted aspects of the wiki with MediaWiki pages…