These two may be related since they occurred one after the other. Maybe entirely not. I'm no programmer.
I'm not sure if it happens every time in these circumstances, but I've had it occur in previous versions. Get into combat and cause the enemy to retreat (in this case, my Lasher took the armor off a Buffalo and a Lasher but the battlescape was too small for me to catch them as they ran). Harry their retreat, then pursue. Get your butt handed to you (damn Buffalos and their ability to fire a massive volley backwards) and decide instead of trying to hobble away in your crippled frigate, you want to reload. ESC, exit to main menu, load saved game. Upon loading you will be taken to the combat results screen as if the enemy fleet you just loaded away from had actually managed to reach the top of the battlescape and burn away. You can interact with all the options, however when the window closes your fleet is right where you left it upon saving.
After all that, I decided to head toward the pirate base. Swung around a couple fleets in a daring chicane, clicked the base for the last inbound leg, and...
2706335 [Thread-5] INFO com.fs.starfarer.campaign.save.CampaignGameManager - Finished loading
2736610 [Thread-5] ERROR com.fs.starfarer.combat.D - java.lang.ArrayIndexOutOfBoundsException: 0
java.lang.ArrayIndexOutOfBoundsException: 0
at com.fs.starfarer.campaign.fleet.FleetMemberStatus$ShipStatus.super(Unknown Source)
at com.fs.starfarer.campaign.fleet.FleetMemberStatus.updateFromAutoresolveData(Unknown Source)
at com.fs.starfarer.campaign.accidents.oooO.super(Unknown Source)
at com.fs.starfarer.campaign.accidents.oooO.super(Unknown Source)
at com.fs.starfarer.campaign.accidents.OoOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.super(Unknown Source)
at com.fs.starfarer.campaign.accidents.AccidentManager.ôÒO000(Unknown Source)
at com.fs.starfarer.campaign.fleet.CampaignFleet.advance(Unknown Source)
at com.fs.starfarer.campaign.BaseLocation.advance(Unknown Source)
at com.fs.starfarer.campaign.CampaignEngine.advance(Unknown Source)
at com.fs.starfarer.campaign.A.super(Unknown Source)
at com.fs.starfarer.new.super.float$super(Unknown Source)
at com.fs.A.oOOO.Ò00000(Unknown Source)
at com.fs.starfarer.combat.D.o00000(Unknown Source)
at com.fs.starfarer.StarfarerLauncher$2.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)
Note this came shortly after a new Easy start, so I had the combat freighter, had swapped a few weapons on the Lasher, and gone up one level. Otherwise brand new.