If I travel through 3d space, will my travel be stopped abruptly if I encounter a 2d plane without space? That is if a 2d plane of space is missing?
The 2D missing plane is an interruption of continuity in the 3D space you are moving in, so essentially your body just disappears as it moves out of the 3D space. It doesn't reappear on the other side because continuity has been interrupted.
For all intent and purposes, the part of your body out of your side of the 3D space would have disappeared altogether. It would be as if your body had just lost one half.
If you stayed only a few seconds half-in, half-out, then some of your blood for example would keep moving out of 3D space and disappearing. Your blood pressure would drop very quickly and you would probably die very quickly. An eyeball half-out would also empty like a glass of water tipped 90° to one side.
If you kept moving, for example from inertia, you would just completely disappear never to come back.
It all depends of course on what you mean exactly by a missing bit of space, but this is what would happens if this bit of space really no longer existed.
Maybe the really interesting question rather is what would happen to space itself. If space does not exist in itself, that is, if space is an epiphenomenon, then it cannot go missing either, so that would make your hypothetical scenario totally impossible.
If there is, however, something like the fabric of space, then such a space might conceivably be inside another space, for example a 4 or 5D space or whatever. In such a case, I think the effect of a missing bit in it would broadly be the same as the one described above.
The more plausible situation, however, is that spacetime as we think of it, including in General Relativity, is essentially a model based on empirical experience, empirical experience we have no means of deciding whether it is complete of reality. So, we can only answer this sort of question on the basis of what we understand, i.e., on the basis of our model, and scenarios that are counterfactual to our model, as this one is, have almost zero plausibility. The answer can only be as good as our model and our model is most plausibly false of reality, even if it is true of our empirical experience.