If they're firing at your ship, they're already hostile, I'm not sure sacrificing your ship will help (except they can't follow it to your home system).
Slow down, lower shields and go off at a 90 degree angle to your current course. It should make you disappear from thermals.
I don't have shields. And honestly at this point it is really hope they don't run out of missiles before I get to the jump point (not likely) or just give them my ship now.
If he is concerned about getting rammed, presumably the ship is well within range of enemy actives so reducing passive emissions probably wont do too much here.
Currently in game I have a ship running away while a newly discovered race fires missiles at it. The missiles can't do anything because I have CIWS on the ship purely for this situation. The problem is it appears as though they will ram me before I am even able to get out of the system. I just came up with the idea of turning sensors and the transmitter off, but I don't know if they will still be able to detect me. I just saw the option to give the ship to another empire and I thought maybe that would be a better idea, because if my empire hates them for destroying a ship then things would not be good. So what do you think, is it worth it to sacrifice a ship so your empires have a better chance of working together?
Edit:I tried turning the sensor and transmitter off and the enemy can still see me.