SIPC. The securities you own (by way of the mutual funds) are isolated from Vanguard's corporate funds. In the event Vanguard collapsed, SIPC steps in and ensures each investor is given their proper holdings (stocks, bonds, cash, whatever) that they legally own.
Per FINRA regulations, they are not allowed to commingle your securities with their securities, nor lend them to anyone else (unless you bought stock on margin or sold stock short, then they can lend out only an amount appropriate for how much you borrowed -- not your entire account).
MF Global did violate this FINRA requirement (no idea why Jon Corzine didn't land in jail for life -- guess he played the "I'm just some idiot they pay $8M a year to look pretty and not actually know what goes on here" card really well), but SIPC stepped in and ensured customers were made 100% whole (except those that sold their interests to vulture capitalist for pennies on the dollar -- but they screwed themselves).
So if Vanguard collapsed, and they ceased activities, you would likely end up with a large assortment of various stocks & bonds based on the funds you owned -- assuming a Fidelity, BlackRock or similar didn't buy out their business and roll their mutual fund assets into similar mutual funds that they ran, leaving you with shares of their mutual funds.
Vanguard also has a unique position in the industry as customer-owned, so its shareholders are their fund investors, so they have no real motive to screw customers or take large risks to appease shareholders desires for quick profit.