What happens when a subsidiary distributes its shares to its parent company? After a subsidiary company spins off from its parent and becomes public, what happens when the subsidiary distributes its shares to the parent firm's shareholders at some later time? 

What I'm reading seems to suggest that the price of the subsidiary's stock will converge to that of its parent, but I'm not sure why. Can someone elaborate on this? 

For context, I'm reading a paper on limitations of arbitrage that studies events where the market value of a parent company is worth more than that of its subsidiary.
The argument to have both share values converging is based on the fact that when the subsidiary redistributes the shares to the parent is similar to "unspining off". 

The spin-off subsidiary is effectively being re-owned by the parent, becoming a part (a share) of the parent. As such, owning shares of the subsidiary becomes a proxy of owning shares of the parent.