The PE sales pitch is often that the target company can benefit from expertise management and/or there is value locked in it that can be captured. Both of these claims are... marginal? Studies around the "expert management" claim tend to show this is not true, based on pre/post returns, but it's hard to account for the long term, because PE also tends to focus on sales with very specific characteristics & time horizons (and associated cost savings) that benefit a 5-7 year fund that sells the portfolio company (wait for it) around years 3-5.

Which is a long-winded way of saying the bag holders are anyone invested in the long-term success of the company: 1. employees, 2. customers, 3. owners (i.e. the next PE fund) when the music stops, i.e. what we saw when interest rates went up impacting debt financing, and (real or not) AI-eats-SaaS impacted valuations. I'll add 4. "the public" if the company is big enough, with various levels of goverment and employment, taxes, etc. lost but I think it's more the smaller organizations in aggregate that hurt at this level than any specific company.