They owe folks money. If you buy them, then you owe those folks that money. So you'll have to pay the purchase price, and then pay the company's debts.
How is this the case whenever apparently Credit Suisse investors are not made to pay Credit Suisse debts?
E.g. Saudi National Bank, who announced no more cash to CS
That's the whole point of corporations - that the only thing available for debts is the assets and equity of the company, not the assets of individual shareholders, execs or directors (unless there are some very specific circumstances, which is called "piercing the corporate veil).