You can continue to run older versions of nodejs and NPM just fine. Once they are installed, they don't require any other outside resources in order to run. They run locally using only local resources. And, older versions of nodejs or NPM can still be installed somewhere new if desired/required.

An older version of nodejs or NPM will not just stop running because it's no longer supported. There's no outside dependency that tells it to stop running when it reaches end of life. If you noticed something like that happening, then it is probably just a coincidence and something else changed in your system or configuration that caused it to stop working properly.

Now, there are plenty of issues with running older versions of nodejs that you have to be aware of.

1. You don't get security updates.
2. You don't get updates to adapt to OS changes.
3. You don't get bug fixes.
4. The current versions of NPM modules you are using may no longer support your specific nodejs version or a more modern OS version. You can, of course, continue to run older versions of modules too, if desired to maintain compatibility with your older version of nodejs, but those older modules will have the same possible issues mentioned here as an older version of nodejs.

To me, the biggest risk with holding on to an older version of nodejs is that at some point a serious security risk will be found and you will HAVE to do something about it. With no official support for that security fix in an older version of nodejs, you will have to either manually fix the security vulnerability yourself in your current version of nodejs, change your code in some way to protect against it or upgrade to a newer version of nodejs that contains the desired security fix. The longer you wait to do this, the more potential issues you may find in bringing your software up-to-date.

In my book, it's better to continually move your software forward with supported versions of nodejs. You don't have to do it frequently and you don't have to run on the latest/greatest version, but there are significant benefits to always running an LTS version.