Neb. Rev. Stat. § 71-15,135

Households which are already in occupancy or are receiving assistance but which become ineligible for occupancy or other assistance by reason of income may continue their occupancy or receipt of other assistance at the discretion of the local housing agency for such period, upon such terms and conditions, and, in the case of continued occupancy, in exchange for such rent, but not less than any applicable minimum rent, as the agency shall determine to be appropriate.