A Final Draft single-user license isn't subscription-based, it's a one-time purchase. It's yours to use as long as you're running it on a computer on which it's supported.
Final Draft is not guaranteed to work forever or on any computer it's installed on.
If you have Final Draft activated on a computer running a certain operating system and this computer is never intentionally or unintentionally changed, FD should work on it for a long time. However, if you try to run an older version of FD on a computer or in an operating system that's too new for it, or if you install a new version of FD on a computer that's too old, it won't work. It's not that the license has expired, it's that -- like any other piece of software -- FD can only run on computers it was designed for.