Given the opportunity to park money with the world’s largest private equity firms, ordinary investors rushed in. Getting out might not be so easy.

The private equity firms began to seek out smaller investors almost a decade ago. It was a major shift for firms such as Blackstone, Starwood Capital Group and KKR that had previously been funded by enormous pensions, endowments and sovereign wealth funds. But it was also a way for the big fund managers to grow their assets and rake in ever larger fees.