Keep in mind up front that the landlord can make an offer of the type that was made, and see if the tenant accepts one of the proposed resolutions. If the tenant opts to buy the house, or opts to take $500 and move to a different house, then that will resolve the landlord's problem whether or not the landlord could impose one of those resolutions if the tenant says "No". If the tenant would be content to move, but not for a mere $500, then the tenant can negotiate for more money. The tenant can also negotiate for a lump sum payment and a complete release from any obligation under the lease, rather than moving into a different property owned by the landlord.

Absent something to the contrary in the lease agreement, the lease will carry over to the new owner. With a long-term lease, that's likely to affect the marketability of the property, hence the landlord's concern; but that's not the tenant's problem.