If it's connecting to the internet - Yes

If it's fully offline - No

This is a very unsatisfying "it depends" situation. Is there any app in particular you're looking at?

Some - yes. Others - no.

If it's an internet-facing thing, it probably has security holes in it, so a trickle of fixes is reassuring.

If it's a game, it might just be complete, finished and done (think chess), or it might get occasional content updates (moar different kinds of swords!) or it might get the occasional bugfix or a port to a new platform.

It's OK, in my eyes, even desirable, to be feature complete, and to have no bugs.

You're delving into the unpleasant realm of risk assessment. How likely is the app going to be targeted by a threat actor, and how badly could they use it to damage your data or system?

If it's a public facing service, I'd immediately check if I have alternative applications I could migrate too. Any hold an outsider gets through the public facing app could be used to pivot further into my network.

If it's something that doesn't interact with the network at all, then I wouldn't worry nearly as much, but might look for alternatives any just because I know this isn't going to get improved at all. Somewhere in the middle, you need to decide how much risk you can accept.