No, the controlling Major Power can rebuild destroyed Minor Power units. In your example GE can add Finnish units to its force pool and rebuild them, chosen randomly force pool by force pool. If you need urgently Finnish troops you could consider to buy Ski Div, as they are guaranteed Finnish.
Do you have to do something to add them to your force pool? like in my game atm the Commonwealth should have some Greek units then to rebuild, and Germany some Romanian ones (if you really wanted them...) but I dont' think Germany or the CW has ever made one.
There was that 'add Polish units' action the Commonwealth gets to take, I don't remember something similar for the other minors though?
On the production form, the bottom button of the list on the top right is "Add minor country units". Hit that, and go from there.
Once you add units, you can't undo it, so be careful. There are a lot of countries, for both sides, that you really don't want their units in the force pool.
I thought I knew how to play this game....