Think of the polar vortex like a cylinder full of cold air. If you cut the cylinder in half and move one half away from the other, the cold air will sink.
If you have displaced parts of the stratosphere, the cold air that is held in the polar vortex will be released and flow down into lower latitudes.
If the PV is displaced enough, it may collapse altogether, leading to an icebox solution over parts of the world.

[link to theweathercentre.blogspot.nl]