Not something that's likely to happen in the real world, but The Hunger Games, for all its gritty bleakness, comes from an honored tradition of fantastical worlds and epic quests in which a charismatic young woman is practically required to have an inborn quality that leads an equally charismatic animal to bond with her. Introducing the character through her acquisition of a four-legged sidekick is a great way to kick off her journey.
Except do you remember what happens then. That's right. Katniss KILLS THE LYNX. She gets her animal companion and she SHOOTS IT DEAD. She likes it well enough, says it's good company, but it's scaring off the game so oh well, TIME TO MURDER YOUR FAMILIAR AND GET ON WITH YOUR OWN DESPERATE POVERTY-STRICKEN EXISTENCE.
So if you were wondering why the odds never seem to be in her favor, there you go. She broke the rules before the narrative even began.