Is there anything I can do about thieves in A Dark Room?

As the story progresses, you will eventually be given a choice of how to deal with the thief. So keep carting wood (that's the mechanic that progresses the storyline) to get to that point. Spoilers on the choices below.

Eventually your village will catch the thief and give you the choice to either hang him, or let him go. If you hang him, the thievery will stop and you will receive back the stolen goods. If you let him go, he will grant you the Stealthy perk but keep the stolen goods.