South really doesn't want to leave partner in 1NT but what choice do they have?

Pairs not playing transfers should bid 2♦ as a weak take-out which has to be passed by partner. If you are playing transfers then you cannot take that route to safety. If you have another mechanism for getting to 3♦ as a weak take-out should you use it?

I think not. You only have five Diamonds and 1NT hasn't been doubled so I would pass and keep my fingers crossed, partner may after all have only two Diamonds. Had East doubled then you have to escape to 2♦ . Either by bidding 2♦ directly if you play that as a natural bid or by bidding 2♣ as a transfer to 2♦ if you play 4-way exit transfers when partner's 1NT has been doubled on your right.

Should West enter the bidding after 1NT - Pass - Pass? I think not. West has a weak hand and South may be passing 1NT with as many as 10 points.