Exactly, the problem is that the government is supposed to own the property, but somehow the tenant should also retain a share. If the government buys the share back, then the government basically ended up gaining net 0 dollars, the full mortgage is still due.

The only way this could work is if the property was sold to a third party and the profits of the sale were distributed according to how much you paid in, the obvious problem with this is that the government won't own the property anymore.