Are we about to see a run on Private Equity?

There are now hundreds of PE shops, just in the US, and we're coming to the end of the ZIRP/Fed liquidity bonanza era. In peak years, PE was dumping 90% of their capital into (often) low-margin software firms. It's easily their largest allocation, as high as 58% of transaction last year. And now the AI reaper is knocking for SaaS and Enterprise software... If today was the public investors swarming the exits, are the big boys on the phone with their funds ordering redemptions? Bonus points for responses from folks in the industry.