They aren't subject to regulatory requirements the way normal deposits are, but they are still limited by the kind of normal sense a manager would have over trying to keep the $1/share price. Can a MM fund blow up? Sure, if there's a run on it. But if there's a big run, there's bigger problems to worry about than these guys who want to make a few basis points on the overnight rate. Hard to believe the tedium, but there are actually guys out there whose job it is to buy short-dated paper all day every day.
Anyway, in any extreme crisis it's unlikley those funds would be tapped (I guess BofA considered it briefly when it's investment in David Shaw went south during the same time as LTCM; outrage was high and they quickly moved away from that idea). When Citron blew up Orange County, it was actually the tax-free MM funds who did well in the scavenger hunt that happened as they unwound his positions: Fidelity's CA Tax-Free MM fund went, for a few weeks from something like 3.1% to 5.2% ... you can't say those holders weren't happy to see a bigger yield that month.
/jordan