Keeping a hold on this chaotic mess is the Warpfang Bank, famous for always actually getting what they're owed back. There was consideration of making 'The Warpfang Bank gets its due' an official motto, but it was discontinued after several dwarf banks threatened to sue. Dwarven legal suits being perhaps the most feared weapon on the financial market, even the mightiest bank of the Skaven was unwilling to push the issue.
Rather than attempting to impose any sort of regulations on the market, the Warpfang Bank controls it by being the biggest rat in the sandbox - almost every Skaven in the under-empire owes the Bank money, some even from birth as their birth breeders were bought with loans from the Bank. With that level of control over the cashflow, and extremely vicious and well-equipped collection officers (often better-armed than most military forces due to the Bank's hefty involvement with the four Great Clans), the Bank indeed always gets its due, even if it can't say it in that exact sequence without a fine.
The IOUS can also be redeemed in other ways than material possessions or work - sufficiently useful tasks accomplished may be judged to be equal to the debt owed. Of particular note is the first Skaven Civil War, where the then-Council of Thirteen collectively dumped all their debt onto the newly-revealed clan Eshin, who promptly paid it all off by assassinating most of the warlords and clanleaders under Pestilens.
Of course, with such a fluid system as this it's perfectly possible to cheat it. With enough legalese a Skaven may be convinced that he or she owes the Bank much more than they actually do, and they aren't afraid to utilize this strategic records-editing to apply political pressure on their rivals. And it's generally tolerated, for no matter how exploitative the Warpfang may be, the alternative of a free market composed of Skaven is far worse.