Say I sue you successfully, and the court delivers a judgement that awards $1000 in damages. It is not the responsibility of the small claims court to ensure that the judgement is fulfilled.
In fact, the debtor (person who lost) can outright refuse to pay the creditor (or the person who won). They are not in violation of any law at this point.
However, the creditor can ask the court for options on enforcing their judgement, and these can include, but are not limited to:
- Garnishing wages
- Providing a court order
- Seizure of assets (through court sheriff, don't use this yourself or you end up getting into criminal matters)
and others to enforce the judgement. The debtor isn't liable for refusing, unless when they are in violation of a court order. Violating a court order is a criminal matter, and the debtor could possibly be found guilty of contempt of court.
Oh, and the case wouldn't move on to a higher court. Cases go to a higher court when an appeal is made, generally when there has been an error in enforcing the law. You also need to be provided leave to make an appeal.