I wasn't saying it stopped at B. Beyond B it would just continue on its merry little way.

So at least in one dimension it is an infinite line, where it cannot be localised anywhere along the line.

I don't see any reason why it should not be stationary in a higher dimension. In 3 dimensions it is perfectly OK for an object to travel on the x axis, but be stationary on the y and z axes.

It is an interesting possibility, because such a scenario would lead to some interesting (and possibly testable) possibilities.

Since it is assumed that a particle that is superluminal can never travel at subluminal speeds, and visa versa; and that superluminal particles have imaginary mass while subluminal particles have real mass, so we are now speculating about a particle that has imaginary mass in one dimension and real mass in another dimension, and that this situation is inviolate (i.e. the dimension in which the particle has real mass can never become imaginary mass, and visa versa).

By comparison, conceiving of a particle that has imaginary mass in all dimensions is fairly straight forward (particularly if you cannot localise that mass), but how would a hybrid particle which contains both real and imaginary mass vectors behave? Could energy be transferred between the real and imaginary mass vectors of a particle? In fact, one of the very novel parts of this scenario is just that mass must be treated as a vector quantity, whereas we tend to think of mass as a scalar quantity.