You can set a script to run when the file is opened that looks like this:
If [YourTable::Expirydate < Get ( Currentdate ) ]
Show Custom Dialog ["This system has now expired"]
Of course, some people may figure out that they can get around this by resetting their system clocks just before opening the system and then they can reset the system clock afterwards. To stymie that trick, you can build this same check into other frequently performed scripts throughout your system so that it not only checks the system date but frequently rechecks it.
If you don't already do this, you'd also want to strip out the admin account so that they can't purchase FileMaker Pro and use it to open your file and then disable this check in your scripts.