Around here, if an abandoned car, (which is what happenned to this Plymouth) is left on a street, it will be ticketed. Then after five days, towed to local towing/storage yard. If tickets and storage go unpaid, yard owner turns in paperwork to apply for a salvage certificate through DMV. Then this car can be legally parted out then junked. Once a salvage certificate has been issued, it can NEVER be legally titled/registered again.
I would say that the Plymouth went to the crusher, as nobody back then noticed the odd VIN on an old FOUR DOOR car! We got the story here straight from the last owner, car stolen and insurance claim paid, face it-she's went to junkyard/scrapyard once insurer paid for it. Same way it's done today. Odds of this car existing is impossible. Low probability of ever even knowing the VIN. A great story, but beating a dead horse...