If you're looking for an analogy, how does a guy with negative to very small net worth rent money from a bank to buy a $1M house?
If you're using "how" as a proxy for why, well who knows why. Or as a proxy for how come our economic system permits this kind of thing, long story.
One cornerstone of our economic system is bad money always chases out good money. If your competitors are leveraged up, you MUST leverage up, or you'll get bought out and levered up like everyone else. Much like one guy willing to take a subprime mortgage doesn't move the market, but if enough people do, then you must do so or not play.
So someone thinks they can pull enough cash flow and/or increase combined net worth enough to both pay off some banks AND make a modest profit for themselves. Well, given the remarkable lack of diversity at high levels, executive drones are all interchangeable with all other executive drones, so I personally find this an unlikely outcome, but at least that is the theory.
A leveraged buyout (LBO) is when a company ... is purchased with a combination of equity and significant amounts of borrowed money, structured in such a way that the target's cash flows or assets are used as the collateral (or "leverage") to secure and repay the money borrowed to purchase the target-company/asset. Since the debt ... has a lower cost of capital ... than the equity, the returns on the equity increase as the amount of borrowed money does until the perfect capital structure is reached.
In other words, you load up debt on the company that you're acquiring with the hopes that the amount you're going to make running that company is going to be more than the amount it's costing you to service the debt.