Couple Rings. Last I checked, it’s pretty common for korean couples to buy each other rings to signify that they’re in a relationship. And now that Sangwoo and Bum are “married” it would make sense that Bum would want some object to represent that bond.
We have a couple hints to Bum purchasing this gift.
Chapter 57, Bum looked at her hand, but besides noticing the bruises look what else is in focus.
A ring.
In the past Bum had also tried to give his first love a ring,
But we all know how that had turned out. But this time, things are different. This time he’s with Sangwoo.
Now what about the time constraint? I think Bum wants to give the ring to Sangwoo on his own birthday (which is why his birthday is spoiler). Bum isn’t someone who likely celebrated his birthday a lot, but turning his birthday into a day to celebrate their relationship is something I can see Bum doing. I can see him wanting to turn this day into a celebration of their bond.
Bum has already given his death to Sangwoo, why wouldn’t Bum give the day of his birth to him as well?