Ok look at it this way. Does your lease with them allow them to sub lease? Is there going to be a new person added to the lease, or they are going to lease it out without your approve. There is a Major problem with this, is if the sublease/ unauthorized person moving into the basement any injure will fall to you. Any damage to property that is beyond the amount of deposit will be a problem to get because "it's not your tenant." You can go after your current tenant, but that will cost money and court time which will it be worth it?
So the major problem is Liability here. If there is a fire, from basement, due to unauthorized dwelling, will your insurance pay for it also?
You can bite the bullet here, and the final decision comes from you.
For me, it's cure or evict. I bought single family because I want to deal with single family, if I want to deal with multifamily headache, I would gone and bought that.
So main point is your Liability vs Reward worth it or not.