The locket can be given to Elisa when she arrives on day 26. This is not mandatory and does not affect the outcome of Elisa-related events.
If Sergiu is alive and Elisa's entry is allowed, Elisa will thank the inspector and keep the locket. If the inspector keeps the locket or denies Elisa's entry, Sergiu will ask the locket back a day later if he is still alive.
If Sergiu is dead and the inspector does not give the locket to Elisa, it will remain in the booth for the rest of the game, but does not have any use and does not affect gameplay.