Yes your criminal record remains after destruction. Earlier in the game I did some things in Asellus Primus and built up a bounty of 350Cr against me and for reasons known best by the station (could have been stolen goods or flying weapons out in the no fire zone) I was destroyed by the station.
My wanted status had gone and I went happily about my business. Then I checked and found I still had outstanding fines against me and 0.45 hours to pay. As I had some business there I settled up with local law enforcement. I haven't tried leaving them unpaid, but I presume that once the time limit (24 hours iirc) has passed you go back to wanted. I don't know if they add any extra penalty for failing to pay the fines, maybe someone could try that?