Permanent THR displacement can occur for reasons other than the existence of a (new) obstacle. In my part of the world, the most common reason for it is pavement failure and lack of money to effect repairs. That is the case at Momote airport, on Manus Island, where the remaining length isn't especially critical.
It was also the case at Daru for many years and continues to be the case at Port Moresby, for RWY 14R/32L, which now has a very restricted length and limited to aircraft with MTOW below 5700 Kgs. In this latter case, the T-VASIS was decommissioned (Daru has never had VASIS or PAPI) while, at Momote, the T-VASIS was relocated at the 34 THR end and subsequently replaced by PAPI.
Before escaping from Port Morbid, I put the question to our Air Nav Services people ... What is the procedure in the event that a permanently displaced THR was needed at a place served by an ILS? Their answer was to turn off the GP and VASIS/PAPI and issue a Notam. I suspect that this answer was based on the known fact that money would not be rapidly forthcoming to enable resiting of those facilities.