This bug https://bugs.mysql.com/bug.php?id=80821 reported by Philip Stoev affects Percona Server as well.
Quotation from his description and test case:
If two tables are in a foreign-key relationship and a multi-table DELETE statement operates on both, replication will break.
2016-03-17T07:35:58.415740Z 8 [ERROR] Slave SQL for channel '': Could not execute Delete_rows event on table test.t1; Can't find record in 't1', Error_code: 1032; handler error HA_ERR_KEY_NOT_FOUND; the event's master log master-bin.000001, end_log_pos 1692, Error_code: 1032
2016-03-17T07:35:58.415776Z 8 [Warning] Slave: Can't find record in 't1' Error_code: 1032
2016-03-17T07:35:58.415787Z 8 [ERROR] Error running query, slave SQL thread aborted. Fix the problem, and restart the slave SQL thread with "SLAVE START". We stopped at log 'master-bin.000001' position 1378
5.6 does not seem to be affected.
How to repeat: