The Korean says 'GOM' or 'GOEM' if I'm reading it correctly. It's a Gee sound an Oe sound and an M sound. No clue what it means.
Also sorry for your loss but wow what a find. I hope people point you in the right direction with whatever you choose to do with the shoes. Whether NIKE intervenes, a classic collector makes an offer or something else, I hope they find a good home and you can take some solace in the 'joy' these shoes and your family have brought to internet strangers.
Well, based on your assistance....one possible translation of the Korean kanji is "Friday". So, I check a 1985 calendar with the date printed on the shoes 85-06-08 and if 06 represents the month June and 08 represents the day.......that would have been a Saturday June 8 1985. If the date is August 6 1985....that would have been a Thursday....Really!!!....what are the odds of this..???.