The Depository Trust & Clearing Corporation settles most listed securities transactions in America; in 2011, it did $1.7 quadrillion [1]. You've never heard of it unless you're a professional trader, but it's actually quite fascinating to read up on.
Trading looks instantaneous. But settlement takes a few days. In between are a series of credit agreements. From your broker to you. From the clearinghouse to the brokers. DTCC is the clearinghouse. Robinhood is the broker.
There are clear rules and contracts between DTCC and its members, including Robinhood [2]. Those contracts ensure that when you buy shares through your broker from a Robinhood customer, if Robinhood falls down two days later, there is collateral sufficient to make you whole. Those collateral requirements change in reference to, amongst other things, the volatility of the security. (If something goes up and down more, ceteris paribus, small mistakes are more likely to become firm-ending ones.)
Again, these are well-known formulas. Unusually, however, Robinhood didn't build this into their fee model. Given market makers, their revenue source, stopped making markets in GME on account of how volatility effects their risk profile, executing GME trades would leave Robinhood sending orders to an exchange, which may cost money, and ponying up collateral, which also costs money.
In my opinion, that's what they should have done. Most brokers have policies for these situations. Higher brokerage fees for securities on a schedule. Not making shares and cash from trades available until the trade settles, sort of like what banks do for large cheques. But I don't know if Robinhood is able to do that quickly. So instead they pulled the plug.
[1] https://en.wikipedia.org/wiki/Depository_Trust_%26_Clearing_...
[2] https://www.dtcclearning.com/products-and-services/settlemen...