Tenants never signed the lease but are still paying rent?

[Joshua Penners]

Hello BP community. My dad has been an accidental landlord of a SFH in another state and has been collecting rent through a Property Management Company in the area for the past 10 years. A few months ago my dad and I decided to get ourselves educated about REI and coincidentally noticed that the current tenant is living in the house without a signed lease. This had fallen through the cracks with the PMC and they had never notified us about it. The tenant still pays rent. However, when we asked the PMC to get them to sign the lease the tenant refused. Our PMC advised us to give the tenant a 30-day notice to vacate and we gave them the go-ahead to do so.

Is this a situation anyone here has encountered? Are there any complications you can foresee? The state is AZ. Thanks for reading!