Tenant Remaining Post closing

[Alex Del]

Hi all, 

I am looking to go under contract for a property that has 2 units and needs some work to bring it up to speed with what the current market in the area offers.  However, in the unit that needs the most work, the seller isn't interested in not renewing their lease (month-to-month).  They have been in the unit for about 20 years, there is no security deposit on file and what they pay is hundreds below market value.  Would it be stupid of me to close on the property with them in place and not renew their lease myself?  I feel like that could open me up to a ton of potential problems, such as them deciding not to pay the rent, going through a lengthy eviction process, a judge siding with the occupant due to their time in the property and community.  

Any advice or experience would be greatly appreciated.  At this point I may be walking away from this one if the tenants are to stay in place.