Will changing the Apple ID of a device lose access to the previously purchased apps on it?

The games are tied to the Apple ID that downloaded them. If you changed to your Apple ID, you would not be able to redownload those games. Your only option would be to try one of the three ways to reset the password to the old Apple ID. Which one you are able to use would be dependent on if the Apple ID has a Trusted Device or Trusted Phone number associated with it. The last option is to reset by web access at the iforgot site.

If you forgot your Apple ID password - Apple Support

Apps can only be re-downloaded when a device is signed in under the same Apple ID that was used to download them originally. Just a qualifying statement here; usually people use the same ID for the entire device, but you can sign into the app store with a different ID. So in terms of downloading the apps under the old ID you would have to sign into the App & iTunes store with that ID to be able to redownload them, but that ID would then apply to anything to do with those stores.

All that said, good luck finding apps for an iPad 2 still available. Frequently developers only have a version available for the last couple of iOS versions so don't be surprised if you can't find them.

Furthermore, you will find using an iPad 2 a labor of love these days. You may have difficulty getting access to certain web sites, or getting old version apps to interfacing with the services to which they connect.