S corporations give their owners the same protection from liability as C corporations. Unlike a C corp, however, the S corporation is a pass-through entity: the bookkeepers divide up corporate profits among the shareholders, who report their share as personal income. When an S corporation breaks up, the owners are protected from liability for unpaid business debt. This doesn't always work, though.
When you close an S corporation, you file your dissolution paperwork with the same state where you incorporated. The state's laws tell you what steps you have to take to shut down. In Arizona, for example, the owners or directors must vote to dissolve the company, set an ending date and tell creditors the company is closing. That starts the clock ticking: if creditors don't file for payment by the state deadline, they lose their claim on the corporate assets.
When claims for payment come in, you and the other owners have to go through them and decide which ones are valid. If someone's got a valid claim, you pay it, then on to the next claim until you've wiped out the company assets or paid everyone off. If you reject a claim, notify the creditor why he's not getting paid. If paying debt reduces the company assets to zero, any remaining creditors lose out, because they can't sue owners for the debts.
Sometimes creditors can "pierce the veil" that protects you from liability for the corporation's unpaid bills. For example, suppose one of your suppliers sues you and your fellow owners, claiming you placed an order you knew you couldn't afford. If she proves this in court, the judge can rule that you committed fraud and that you are responsible for the debt. If you fail to follow state rules for corporations, such as holding annual meetings, that can also pierce the veil.
Another way to lose your liability protection is if you don't keep your personal and corporate accounts clearly separate. Suppose you or one of the other owners pays company bills with a personal credit card, or routinely takes money from the business accounts to pay personal bills. A judge might decide your S corporation is just a legal fiction rather than an independent entity. In that case, the judge may side with creditors who want to pierce the veil and sue you personally.