Of course the banks would - they're really loaning the money to the buyout firm, not the company being bought out. The firm performing the buyout makes big money, as do the banks. The firm being bought out is stripped to the bone and charged with servicing that debt. Sometimes they survive and can be spun off into the market again for big profits. Sometimes they limp along in private ownership and make modest profits, all of which go to the buyout firm instead of being shared with public stock owners (or, god forbid, the remaining employees doing the actual work). And often they just implode. The banks take a hit on some of these deals knowing that often they turn out to be quite profitable, at least in the short term - profitable enough for them to be able to afford to write off quite a bit of bad debt.
They're sort of like corporate identity theft rings. A buyout firm is essentially using the good credit of a going business concern to take out enormous loans it couldn't get on its own. They use some of the money for buying the going concern, and then hopefully refinance that debt at lower interest rates down the road, pocketing the difference and using it as collateral for the next buyout. If the debt load implodes the legitimate business they purchased, well, that's just too bad for the American economy. The parasites are off to suck the next victim dry via identity theft. But it often works long enough for them to cash out and use the money to hijack another business.
Remember, the guys running these sham operations are paying themselves enormous salaries and bonuses, regardless of how well the identity theft operation pays out. Even if Dell implodes they still make millions in the process. The success or failure of the companies they took over only alters the magnitude of the payout, not its eventuality.
Where things get interesting is if interest rates start rising again. We've been in a long term cycle of declining interest rates essentially since the early 1980s. That's been facilitating these buyouts for decades now. These gamblers are betting that if they borrow billions today at, say, 6%, they can refinance in the future at 5% and pocket the difference, covering up for a lot of incompetence in the running of the actual businesses they've hijacked. If that changes, expect to see a slew of business that were involved in these sketchy transactions go under - the buyout firms will cut their losses and run, leaving a bunch of investors holding the bag.
Don't worry about the banks, though. If things get too bad they'll just call up Congress and request another bailout, using your retirement money.