A team has finished a game with 0-6-7 runs-hits-errors line 4 times since 1897, most recently Chicago White Sox on 19 July 1912. That is about one every 110,751 team-games.
Box score for the most recent one ↗
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 0-7-0
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes