Technically your account is "safe" as it would be covered by SIPC insurance for equities, although as others here have pointed out you would probably be safer trading with one of the "too big to fail" entities like JPM, GS, etc., because sad as it is to say they will be saved from failure by the government every time, whereas a relatively small operator like IB will not (the moral hazard implications of which are another whole discussion). And even though it's insured with the SIPC, it's no fun to have to go through the process of getting your money back from the regulator when your brokerage fails.
As for the safest place to keep cash in a crisis, obviously that would be in physical cash you keep stashed in your home somewhere. After that, the safest would be short term T-bills through the government's Treasury Direct program.
If/when we see massive bank runs and collapses (very likely IMO), we'll likely see the same happen with brokers as well. And if they're engaging in re-hypothecation and a large number of their clients pull their money at the same time, boom, now you've got a liquidity crunch for the broker and a likely failure event.