A team has finished a game with 0-4-7 runs-hits-errors line 6 times since 1897, most recently Cincinnati Reds on 12 April 1911. That is about one every 73,834 team-games.
Box score for the most recent one ↗
0-4-2 0-4-0 0-4-5 0-4-8 0-4-6 0-4-4 0-4-7 0-5-2 0-5-3 0-5-0 0-5-4 0-5-1 0-5-7
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes