The private-equity owners of Toys “R” Us Inc. are putting together a $20 million fund to make payments to thousands of former employees left jobless by the retailer’s liquidation, according to people familiar with the matter.

The fund’s creation by Bain Capital and KKR & Co. is an unusual move by private-equity owners of a bankrupt company. It isn’t required under bankruptcy law and has no ties to the bankruptcy process, the people said. The funding will be provided by the buyout firms’ general partners, they added.

The...