Your logic is not logical. If these companies were sitting on cash they would not be bankrupt nor in need of Bains Capital.
I’m not privy to the ins and outs of Bain’s capital manipulations but I am a party as a stockholder to one situation a number of years ago. The company I had stock in had been sitting on a big cash reserve , paying regular dividends, waiting to finance projects when economic situations warranted. Seeing the situation some ‘capital’ investors invested their funds in taking over the majority of the board. In no time at all the original company was split and the reserve funds were taken away and I was left with two much lower level of investments. Granted the original company faltered somewhat but the large reserve was gone. I suspect Bain has been involved in similar shenanigans. At the time it was not called capitalization but called corporate raiding and looting.