Depends on if existence in this level of 4D is dependent on being at this level. Using your 2D in 3D example (aka Flatland) what if the 2D plane is at sea level pressure, but changing the Z axis there is a different pressure (as we understand, but the shapes would not), to the point where Mr. Square dies if we lift him too far up.

Now imagine a 4D version, where it's not air pressure, but something more fundamental about physics changes if we're moved from our current 4D state. The idea being that space as we understand it is 3D, but perhaps exists as part of higher dimensions along with other universes. But they could be completely different, and movement from ours to theirs by just sliding in 4D would change the "space" we're in, in a bad way.

Or we could just wink out of this 3D space, but be in just a different state and be fine, seeing a weird cross section of what we're used to.