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The new owner would be taking an "assignment" of the lease as part of the purchase, and would be stepping into the shoes of the landlord and having both their rights and their duties. The lease contract does not have to mention this specifically for this to be true, as this is an automatically applicable doctrine under common law.
if new owner wants to take possession of a unit, the lessor reserves the right to buy out the leasee’s lease for the amount up to 3 months of the lease or the balance of the lease remaining, whichever is less
This is a clause in the contract, I am guessing. This overrides the assignment doctrine, and gives the new owner extra rights to buy out the tenant. No, I am afraid she cannot refuse the buyout if she signed the lease, I am sorry to say - this is a contractual agreement.
While the state may require 60 days notice on a yearly contract, this is different - it would be an early termination buyout - one that the new owner has a right to - and the same 60 day notice would simply not apply here.
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