I have run a small experiment sending a small number of unengaged profiles a Christmas Card email ( elegant graphic, goodwill message and no sales offer or pitch ) The open rate was excellent and unsubscribe was very low. I think this may in part be due to the time of year, most are in a good mood and its less likely to be unsubscribed for the same reason. I think scaled this out to more unengaged profiles and have picked up more than 30k profiles back into temp engaged segment. It will be interesting to see if they stay engaged when receiving campaign emails and will report back with my findings.
You could test this on your list with a Happy New Year message.