You've caught me on the hop here J_T! It's been a real long time since I've had to consider action in the event of a displaced threshold, as regards ILS and VASIS/PAPI. I'll have to study it up and get back to you, unless someone else comes up with the answer, but I'm pretty sure the action differs somewhat, depending on whether it's a short-term temporary displacement, a long-term temporary displacement or permanent displacement.
The first thought that occurs to me, in the latter case, is that the VASIS/PAPI must be resited. This destroys harmonisation with the ILS GP and, if it's impractical to resite the GP (and then get the new arrangement properly flight checked), I suspect that the GP has to be turned off and appropriate Notams issued with relevant document amendments to withdraw the ILS procedure in favour of a LLZ or LLZ/DME approach.
This whole issue relates more to Operational Standards than to basic procedure design. Ops Standards is my area of specialisation, more so even than procedure design, but I haven't had to be too active in it due to the high priority that PNG CAA has been giving to procedure design over the years. So please don't take the above answer as gospel until I can check it out.
My first post was based on Slash's comment, quite rightly, that "Of course this isnt done at night or in IMC for obvious reasons". To conduct that sort of approach at night or in IMC would, most certainly, be courting trouble as there's usually no opportunity to see an obstacle and take timely avoiding action on the lower approach path.
Indeed, to have the GP radiating at all, when the THR is displaced could be a real operational worry. One must consider the lower wheel clearance over the THR and tail strike could become an issue for long body aircraft. Just thoughts off the top of me head at this stage.