It sounds like there may have been an agreement to vacate the premises by a particular date, in which case a notice that utilities will be shut off on or after the agreed date is not unreasonable. However it sounds like the shut-off has less to do with an agreed move-out date than it does with trying to force the tenant to vacate without following proper eviction procedures.

Even a holdover tenant has rights and should be lawfully evicted.

If the landlord does commence an eviction for nonpayment and you wish to retain possession, you'll have to pay the rent you owe.