The lease agreement has been violated by the existing tenant and would be terminated. The negotiation would be for a new lease agreement to include the unauthorized tenant after being qualified for rental approval. The new lease agreement would increase the monthly rent by two hundred ($200.00) dollars and compensation to the landlord for the past unauthorized months of occupancy, which is less costly than moving expenses.
Do not set yourself up for problems trying to ask for any back rent. You have most likely waived your right to it anyway. If you recall, they have lived right above you for six months without you knowing it. Just stick with the rent increase, remember your tenants are disabled and will get a free lawyer if needed. Ask for $150.00 additional per month if they sign a new lease right away. That would bring the rent total to $850 per month. Don't be greedy, be a savvy landlord.