I have a question (since I can't run EDO acceptably enough to test it)- when you are shot down and the police nab you, do ships in your FCs and (more importantly) anarchy systems get impounded?
If it is, anarchy systems are being doubly punished, since they should be neutral safe harbours for criminals. If no safe places exist, criminal gameplay and thinking is being hit.
Not a pirate, but due to the wonky justice system in EDO (it's the same than the one that put a fine for loitering in burning station, just sayin'), I've been sent to space jail more than once after death.
While I don't know about the FC, the ship is left where it is when you die, so is the SRV (but usually they destroy it during the fight). In space jail, you have to get an Apex shuttle to go anywhere, then use Inter Astra thing to tow your ship back. I've heard of some space jail with an inter astra, but never saw one so far.
When you are killed on the ground, you have to pay your fine/bounty when you are sent to jail (no choices), so everything's cleared on the ship you use to commit the crime (or drop you near the crime site).
If you ask about justice system in Anarchy system, you don't get fines or bounty there, on the ground. However, someone reported he had one once, but I assume it's a bug (I've been happily shooting NPC there no problem).