The wealthiest people in the world are wealthy by virtue of the gains made on the assets they already have. So, in a bull market, their assets grow while someone without assets is left behind. The inverse is true, too - they'll proportionally lose to the same degree in a crash - as while a poor person may have no investments, the wealthy person's investments will crash in line with the market. There won't be a financial cushion, at least not a significant one.
Books have been written around timing markets and it's generally accepted that it cannot be done reliably. To get out before a crash then buy cheap would require you to predict three different moments accurately: when to get in, when to get out, and then when to buy on the "cheap". Timing even one reliably requires luck or clairvoyance.
"Rich people have the financial cushion to not be impacted in the slightest way by such crashes". This is clearly false - wealthy people don't keep mountains of cash lying around as they would miss out on the growth in bull markets, and as a result their wealth would decrease relative to their peers.
Investors generally just become relatively poorer during a crash then make it back and more during the next bull market, at least that's how it's worked until now. There's an old quote I can't find the source of right now that sums it up fairly aptly:
"Stocks go down faster than they go up... but they go up further than they go down".