To unlock the "Kolechia Token" trophy in Papers, Please, you must reach Day 25 (December 17th) and soothe a lonely heart.
On Day 25, the fifth person to enter your booth (including Sergiu as the first entrant, if he is alive) does not have all of their documents but tries to sway your opinion with a blue love note. Whether you choose to allow or deny entry, make sure to keep the note. (You'll get a citation if you let them in).
The seventh person in the booth starts lamenting the fact that nobody loves them after stating the purpose and duration of their visit. Give this person the blue note to receive the Token and unlock the trophy. Check their documentation, there's a small chance that it's invalid.