Is there a way to make it so a player cannot un-burrow a unit, when it is owned by them.

Other then making it un-moveable once it becomes un-burrowed? Thanks.

Try using Burrow Detection;
http://www.staredit.net/maplantis/index.php?sid=81c00c12ae;wiki=77

Once you detect that the unit is unburrowed, you can remove the unit, and replace it with a burrowed one.

whats your situation?
how come you cant make burrowed units unmovable?

Hmm, if no one else knows a better way I guess I'll do this. Thanks.

Create unit by a computer with burrow, give to player who has burrow disabled.

I have 4 different units, which are given for a point system.

And at a specific time I need to give these units to the specified player, then calculate who owns the most.

And I need them never to move.

Zachary's answer fixed my problem, thank you.

Aren't computer players still unburrowing altough they shouldn't be able to?

yes, but humans can't unburrow.