Does a polyethene shrinking signify negative or positive entropy? When I think of something shrinking, I would intuitively think it decreases in entropy as there is less movement. E.g. if a gas was to reduce in volume, there would be less movement of the particles and hence less entropy.

How about for as solid?

I have read if polyethene shrinks, it INCREASES in entropy.

Why is this the case?
When stretched, the polymer chains elongate and are held taut. This means there are more crosslinks and fewer opportunities for internal degrees of freedom (movement). A relaxed polymer is not held taut and therefore can freely move, having more degrees of freedom, and an associated increase in entropy.