Tenant is never home...we thought unit was abandoned

[Bob Woelfel]

We just purchased a small multifamily building.  One of the tenants in this building is never there....as in for weeks we thought it was abandoned.  None of the other tenants had seen her in over a month.  She rarely if ever sleeps there and doesn't come back to the unit for weeks at a time it seems.  We've owned the building for 3 weeks now and she first contacted me yesterday.  She wants to stay although was way behind on rent with the previous owner.  Her water was cut off as well.  Aside from her issues in paying and being a responsible tenant i'm looking for blind spots here.  What issues might come up with a tenant that is never occupying the unit?  I'm aware of utilities and issues there, but I'm just wondering how big of an issue should I make this with her.  We were going to evict and still might, but I have a meeting with her to discuss her tenancy.  Any thoughts are appreciated.