Tenant told me someone broke into her unit - suspicious...?

I noticed that you mentioned that she had some disabilities. It may not have occurred to her to call the police or she may have some unreasoning fear of the police, who knows. All I am trying to say is that there may be many reasons why she didn't call the police. As the landlord, I would fix the door and call the police myself. Let them know what happened and hopefully they can give you more information after their investigation. Good Luck!