Ok, I did a little testing. Once victory conditions are met:
Ships can still move, use supply, get resupplied, engage in combat, be damaged, be destroyed.
They cannot be repaired. They can be retrofit, but the new components will not be repaired.
Resources will not accumulate or be used. If you are running a positive resource flow your resources in storage will not go up. If you are running a deficit because of ship maintenance you will never run out of resources. Not sure if you are already at zero and running in the red on reources if ships will still be abandonded. You can scrap of fire on to destroy ships though.
Nothing will be built in any queues, even though you can place thing in the queue and it will look like they are going to get done. But no work is ever done on them, similer to repair.
DId not test research or intelligence. I suspect they are the same. Resaerch is pointless since you can't build anything or upgrade facs anyway. Intel might have a use, although I doubt it will work.
You can change treaties with other players, but you will nto receive any trade income. Even though it will show on the balance sheet. Your resource storage totals dont' change form turn to turn.
I could see perhaps an interesitng way to finish off a game like this. Kind of a state of entropy. You will be stuck with whatever you have left at the end of the game. Able to destroy your opponenets planets and ships, but not to replace or repair those of your own that are damaged or destroyed.
Psychic insurection would be very valuable in such a finish, since it could capture enemy ships without needing to be repaired as boarding parties would. Intel as well if it worked. Need to test that sometime.
Geoschmo