Unauthorized tenant and late rent

[Jon A.]

I have a tenant that has always paid on time and been in the home for almost 4 years. Actually, she has been late once and I waived the late fee because I consider her a good tenant up until this point. This morning ( the 6th) I received a hand written note in my mailbox form her stating that she is sorry but she is late with rent and will pay as soon as she can and that her phone is lost and she is in the process of having it replaced therefore she cannot be reached by phone. She asked me to email her with my info so that we could discuss what is happening. She stated that she got a room mate this past month to help with her bills and that it was a bad decision on her part and that she is trying to have this person removed and assures me that he will be gone and she will pay her rent ASAP. Of course in my lease, there is a paragraph that says no subletting is allowed. 

I immediately emailed her the following:

"I am sorry to hear about your room mate situation. Feel free to let that person know that I do not allow subletting in any fashion. Therefore, they do not have any rights to the property at all because they cannot produce a lease from me. I will evict if need be. My phone number is below. "

So my problem is two fold. I have an unauthorized tenant apparently living in the house as a room mate who is apparently not paying my initial tenant. Which, is obviously not my problem. I am going to issue a pay or quit this afternoon as it is the 6th day and my lease offers a 5 day grace period. The second part of the problem is that the tenant has been a good tenant up until this point and I would like to keep her, but I think she is leaving me no choice but to push forward with a pay or quit notice, followed by an eviction. 

How would other landlords handle this? This property is located in North Carolina. 

Edited to add the fact that my lease has rolled from a year long tenancy to month to month.