Do you owe the debt to American Express? It depends on the state in the US, they can sue you, and try to garnish wages and take assets that way. But some states have laws against things like wage garnishing, it also costs money to sue some one. So if $costToSue > $expectedDebtRecovery they aren't going to sue. They usually just sell the debt to a collections agency who just calls you relentlessly trying to get you to pay, and since the collection agency bought the debt so cheap, they aren't going to throw more costs to collect the money by suing. If they can get any money out of you just by calling, it's a win for them.
Source: Canadian, walked away from my student loan debt after injury, provincial loan was wiped clean federal loan had to be paid off. Student Visa wiped clean. To be clear I could not work and the bills kept getting harder and harder to pay. I was dying with stress and anxiety about bills. So I stopped paying them and bought food instead. I was young and not prepared for emergencies but it was clear I was sinking. I would like to also add this is NOT a great solution if you can avoid it. Responsible spending is. With the debt, for 7 years I could not get a credit card or take out a loan. If my car died I had to buy a new one right now out of pocket for work. It is not good. So though I had about 20000$ in provincial loans wiped it took me over a decade to pay off the rest of my debt. Today I am 100% debt free and even have a few dollars. The difference in stress levels I live day to day are huge I can not understate how much responsible spending with in your means can do for a person.