Server 2003 licensing

Hoping someone can help clarify something I have been told.  In short company X is still running a few Server 2003 machines (cringe).  They purchased extended support for a few years but that has not dried up and cannot purchase anymore.

I am trying to get teams to install patches that where released when still under extended support (just wasn't applied back when it came out).  I am being told that as soon as the server reboots the patch will be removed because there is no license.  Cant see how this works. 

Does a server license actually expire?

If it does expire you can't patch it anymore?

If the license has expired does that then mean company X is in breach of licensing?

If a patch was released then shouldn't that patch be installable no matter the age of the server?

Sure Microsoft wants you to update but I find it negligent that MS will force remove a patch if a server is rebooted even if your license has expired.