With any software, you always buy just the license of being able to use the software. You don’t own the software. If Apple has removed it from the AppStore and the developers have not been able to release it on the AppStore again then they’re in clear violation of some terms and conditions, thereby making the said app / service illegal.
You can't legally sign an app with the Apple Developer signing tools unless you have the legal rights to do so. What you are asking about is rightfully not doable. You do not own the app or the copyright and intellectual rights thereto. You purchased a limited use license.