Not the government directly, from my understanding the loan payment comes from the sale amount, before it is applied to the judgment. The property would end up being sold, then minus any outstanding debts on the property, and the remainder applies towards the judgment.
Outstanding loans must still be repaid, creditors don't get screwed just because it's part of a court judgment and seizure, in fact they get an immediate return. Depending on the loan agreement, if there are prepayment penalties for those loans... those would likely apply as well.
So it is technically possible it seems, with Trump's fraudulent property valuations for loans, that he could end up with a negative overall return by selling various highly leveraged property. If they fraudulently valued something at say $600M and got a loan for $500M based on that... but the property is actually valued and sells for $300M, that loan would be underwater, like millions of American homes. He would still owe $200M for that loan, but would no longer have the property.
If all of his properties are massively overvalued and highly leveraged against, he could end up with basically nothing left from this. Forced to declare personal bankruptcy and losing all the real estate. Court judgments for fraud very rarely can be discharged by bankruptcy, so while other debts might be discharged the penalties will likely all apply, regardless.
I believe the sales would count as income for tax purposes next year as well. Just to be another kick in the nuts.