I assume when you say a writ of execution it is a creditor attempting to enforce a judgment. The best advice I can offer is to make whatever arrangements you can with them and don't be surprised if they attempt to access your bank account again. I know in my case I had a judgment law firm accept about 30% of the total if I would pay it in a lump sum. I don't know if you have friends or family that might help out with a lump sum settlement but it can work. If you go that route, get in writing before you send any money especially that they will consider it settlement in full.
I am in California, I assume from your screen name you may be too. I don't believe they can seize your vehicle at the value you say it is, but I'm not sure about unemployment benefits. I know Social Security is exempt. If you have any direct deposit to this bank account you may want to consider terminating that arrangement, but work towards getting this settled. The judgment lasts a long time (10 yrs I believe?) and if they are taking aggressive enforcement action they are not just going to go away based on one phone conversation where you state that you are unemployed.
