A team has finished a game with 0-6-5 runs-hits-errors line 40 times since 1897, most recently San Diego Padres on 11 April 1969. That is about one every 11,075 team-games.
Box score for the most recent one ↗
0-6-0 0-6-4 0-6-3 0-6-6 0-6-2 0-6-8 0-6-5 0-6-7 0-7-2 0-7-7 0-7-5 0-7-3 0-7-4
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes