Interesting question, which could result in multiple outcomes. First we need to understand the nature of a judgment and the status of a judgment creditor and the creditor's ability to take from municipal funds. Likewise, most municipalities are insured at least to some extent. So first, the most straight forward and what happens in most cases - the municipality's insurance
kicks in at some point (some municipality's are self insured to some amount) after which point their liability policies
kick - i.e., the insurance pays the judgment.
Second, municipality's have various funds, most of them cannot be garnished as they are held in trust for various uses (i.e., enterprise funds), but other accounts could be garnished, beyond that however municipalities are like an other debtor, they cannot pay what they do not have. So the judgment creditor would have to continually engage in collection of the debt as the municipality takes in more revenue. The more likely scenario is that some sort of long -term payment plan agreed upon by the parties.
Third, and probably the least likely, the matter is resolved in Ch 9 bankruptcy. I'm doubtful that an otherwise financially solvent municipality would be brought into bankruptcy by a single debtor. The cases you cite resulted from years of financial issues compounding upon each other. In any event, usually on the state's governor can authorize a municipal entity to enter Ch 9, and even then the Bankruptcy judge has a lot of discretion to allow or disallow the bankruptcy. But if this were the case, the debt would be "worked out", meaning it would be paid probably at far less that face value or (less likely) totally extinguished by law.
These are the possible outcomes I could foresee. Hope this helps. Let me know if I can be of further assistance. Thanks.