This seems to occur when friendly stations spawn too close to hostiles.

The station's ships will attack and destroy the hostile station, and keep attacking it after it's dead.

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xephyr on 2/18/2016 12:41 AM:

Looks like this isn't limited to friendlies, either - I found some ares ships attacking a dead Kobol camp.

relanat on 2/19/2016 4:28 AM:

Must be fairly common. I got this as well. Nearest friendly station to the dead Charon Stronghold was 126 ls away.

nms on 3/4/2016 5:09 AM:

Got a save file demonstrating this: http://ministry.kronosaur.com/record.hexm?id=54420

assumedpseudonym on 5/22/2016 10:58 AM:

 This is probably a related issue: Go annoy a station’s guards without destroying them, then head somewhere else in the system. After they get back to the station, they’ll turn around and go look for you again. Station guards attacking dead stations follow the same pattern: After destroying the station, they dock at their parent station before returning to pound on the wreckage.

george moromisato on 6/23/2016 4:41 AM:

Fixed in 1.7 Alpha 2. Thank you!