KUALA LUMPUR—In its final months in office, the government of former Malaysian Prime Minister Najib Razak turned to the nation’s central bank to pay off $500 million in debt owed by the troubled state investment fund 1Malaysia Development Bhd., people familiar with the transaction said.

The fund, known as 1MDB, has been struggling to stay afloat, and the money helped cover an obligation due to an Abu Dhabi state fund at the end of 2017. The Malaysian fund said in December it came up with the money via an “ongoing rationalization...