@Martha T. It is a little late now, but there are a few things that could have helped you stay out of this situation. One is making sure that your purchase agreement states that the seller is not allowed to enter into any material agreements (like signing new leases) without your consent while the property is under contract. Although the seller still owns the property, they can not enter into any agreements that impact your eventual ownership without permission. If you have that in your purchase agreement and they violate it by signing new leases without your consent, you can cancel the contract and get your earnest money deposit back.
The other thing that helps is make sure all tenants sign an estoppel prior to the end of your due diligence period. This clarifies what is in the lease, and it must be signed by the seller as well. Estoppels get everyone on the same page and eliminate confusion about the lease terms.
If your tenant's lease only lists one tenant (not sure if it says anything about not letting anyone else live there), and she is in violation of the lease, you can begin proceedings to have her cure the default, or get evicted. Note verbal notification is no good...must be in writing.
I'm not a lawyer, haven't seen your lease, and don't know the laws in your state, but it sounds like you may have options if you do want this tenant gone.