The property management company isn't really a
company per se; it's more like a conduit for money, an instrument.
If that instrument defaults, it's not of so much concern that a property management company will die; but rather, that the companies who were on either side of it, relying on it as a conduit for money to flow through, will end up illiquid, unable to exchange through that instrument.
On one side, that's large investors, e.g. mutual funds. So the markets will go down.
On the other side, that's the businesses themselves. Having no access to financially-healthy property management companies to rent from, is a lot like having no access to loans: it limits your choices as a business.
Maybe the valuations of these properties will crash without property-management companies around to compete over them, and businesses will be able to afford to buy them directly. But more likely, as we saw in 2007, the commercial real-estate market will just become illiquid, with everyone who is currently holding empty commercial property (i.e. mostly banks, after a presumed default or bailout of PMCs) refusing to sell it "until things recover", so that they don't have to write down a loss. And that means there won't necessarily be any commercial properties on the market for these businesses to buy into in place of their previous rentals.