What the title says. Mike Duncan says that Caligula quickly squandered the fortune left to him by Tiberius and incurred lots of debt. About Claudius, he says that Caligula basically stole most of his money and so he had to go into lots of debt before becoming emperor.
My question is - Caligula wielded absolute power and exercised it regularly by killing whomever he wanted. Claudius was in the imperial family. What being in debt meant to them? Who had the ability to collect it? Why was there even debt when Caligula seemed to have no qualms about just taking whatever estates he wanted. (Episodes in question are 60 and 61)
I can't speak directly to the question of how Caligula and Claudius dealt with their debts. What I can say is that historically, this is really the question with sovereign debt. If I'm a banker and I lend money to a country with an army, executioners, and the ability to print money, what do I do if they don't pay me back?
The short answer is not much other than revolution, war, and refusing to lend them any more money.
Probably the most blatant example is early modern France. Up until the French Revolution, France was a serial defaulter notorious for "bloodletting". They'd run up the national debt. Then they would default, fining, jailing and even executing its creditors. Between 1550 and 1788, France defaulted 8 times. One of its finance ministers, Abbe Terray remarked that governments should default once a century to maintain equilibrium.
Another method of defaulting on debt is debasement of currency. If your money is worthless, so is your debt. Henry VIII practically defaulted on England's debt by debasing its currency and collecting Seigniorage. Dionysus once collected all the money in circulation and then re-issued it with double the value.
Even today, look at all the hand-wringing around the possibility of Greece defaulting on its debt.
Source: This Time Is Different: Eight Centuries of Financial Folly, Rogoff and Reinhart