I think you are trying to be too academic about this. Some procedures have some quite entertaining Missed Approach profiles ( HKG was/is a case in point), but these almost always are predicated on the ILS, or at least the Localiser element working and you being able to navigate accurately.
You are describing a different situation, one where you loose the ILS itself on the approach. Now if you are somewhere with high terrain on either side of the approach track, you've got a really, really immediate and serious problem...........
What do
you think would be the sensible thing to do,
plod on with no lateral guidance down amongst the hills hoping to end up at the MAP,
or initiate an immediate Go Around?