15 Year Existing Tenant w/o Lease- DEAL or DON'T?

[Hilary Stalder]

I JUST closed on a flip I had a lot of money into and am looking to buy my next deal. This time I'm looking for a cash flowing, long term hold to rent out. I found one that needs some rehab but will cash flow, HOWEVER there is a potential snag... there is an existing tenant, with no lease, that pays under market rent (about $400 under market). The listing agent said they are willing to sign a lease if the carpet gets changed out. I'm asking if they would be willing to pay more (currently paying $1000, market rent is $1400 for this property). I'm worried about the implied lease since they've been there for 15 years and also not sure I want to inherit a tenant... 

Anyone have experience with dealing with a long term (15 year) tenant with no lease on a property they're buying? What are the options/laws and is this a GO or NO GO? Would especially appreciate feedback from Floridians that are familiar with our state's tenant/landlord laws specifically related to implied leases. 

Thanks!!