[onaraft]

In general, you don't need to worry about Vanguard or Schwab or whoever provides your particular index fund going bankrupt. The actual assets in the fund don't go anywhere. Whoever buys the remnants of your now-presumably-dead brokerage would probably just carry on maintaining the fund, or it would cash you out if it didn't want to continue to run the fund.

On the brokerage side, SIPC insures securities in much the same way FDIC insures deposits, but the amount insured is significantly higher, though I don't know it off the top of my head. And beyond that, regulations require brokerages to hold client assets separately from the broker's assets, and this is audited. So for the most part, SIPC is mainly overseeing the transfer of securities from a dying brokerage to somewhere else.

So, for the most part, the risk you describe is more about inconvenience than actual material loss.