It is going to be very hard to get a section 8 tenant out of the apartment.
You would have to go to court to get them out!
Section 8 tenants are helped by the Housing Authority. The Housing Authority suggests them to not leave apartment until there transfer is approved by them, they find apartment after or they are evicted by a judge court order.
Especially if they are paying their portion of the rent and Section 8 (the Housing Authority) agency is paying their portion of the rent, you are going to have to give them time to leave.
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Call the nearest housing authority( section 8)

******The transfer takes 6 months for it to be approved!!
**You can give them 100 30 day notice, they will be told by section 8 that if they leave apartment they loose their section 8. That is why they don't leave until their transfer is approved!
They have to apply for a transfer!