Matt Leving from Money Stuff discussed it today (!). If exchanges provide leverage products to customers, they become banks (providing leverage, through funding typically by other customer's deposit).
So bank runs are possible.
Levine spoke about brokerages. When brokerages extend credit, they can be subject to run dynamics. Not exchanges.
There's a reason the perp exchanges have a fund, it's the capital that protects them from losing money on overleveraged customers. Or rather it's the rainy day fund that they lose out of when the delev happens.
Not sure this is related though, mechanics of today are not clear to me from what I've been able to find.