In his 12 years on the job, Justin Berk, a 44-year-old product manager at an insurance-tech company, had seen his employer get bought and sold twice. All he had received in return was a “pat on the back” at a company meeting.

“A pat on the back is nice, but it doesn’t pay the bills,” he said.

When KKR sold his company, Integrated Specialty Coverages, to Onex Partners, the company meeting was much more significant: Berk received 30 months of his salary as a cash bonus as part of a KKR initiative to share its private equity profits with workers at its portfolio companies.

Berk and other long-tenured employees, like Bonnie Stewart, the director of…