The problem is she rented this 4 bedroom house 3 years ago and they owe her over 4000 dollars in back rent.
That's between HER and the tenants she has occupying the house.
Once you buy the house and transfer title, any rent CURRENTLY due after that is owed to YOU, and any past due rent prior to closing is still owed to HER (the previous owner).
If the previous owner has elected NOT to take the appropriate legal action against these tenants to evict them, that's on her. Once you buy the house, evicting them becomes YOUR problem.
As has been stated, any current lease or rental agreement transfers to you intact once ownership is transferred. If the tenants are on a fixed-term lease, you have the right to evict the tenants only if they fail to pay you rent (as long as they are properly informed that you are the one they need to pay now that the house has been sold) or they break another term of their rental agreement moving forward. You can't evict them simply because you want to occupy the property you just purchased.
If the tenants are on a month-to-month rental agreement, you simply need to provide them with proper written notice (usually 30 days, but check with your state's LL/T laws to be certain).