Suppose I decide to use an outdated application for some reason: maybe I can't update it for compatibility reasons, or updates are not provided in the official repositories I use, or maybe I just don't feel like upgrading it because it just works and I see no reason to update it. For all I know, this application might be full of vulnerabilities that were only patched in later versions.
The question is: can I get infected by using such an application if its input data is trusted? For example, I'm not talking about a PDF reader that you can use to open random documents, maybe downloaded from the internet or sent by your friends, because that would be input data that you can't really trust. Imagine instead that you used that PDF reader only to open documents that you have written yourself (so it's trusted data). Or think of offline password managers, where password databases are supposed to be trusted (it's your data).
I'd guess it's safe to use an outdated application provided that the input is trusted and that it doesn't open any ports for communicating on the internet, but I'm not sure if I'm missing anything.