As a member of the society you "own" it but you can't sell that to anybody. Demutualising creates a new public company with shares, which naturally go to those owners. The shares in a public company can be sold. The exact rules for how shares are divided among members would have been in the terms of the proposed demutualisation.
I can probably look it up but I received a not inconsiderable sum of money for my shares when I sold them many years later. I presume my parents sold and spent the money very soon after the plan went through. All members received shares (it would be obviously inequitable to propose that only those voting for the deal get shares if the vote passes, I'm not sure if that would be straight up illegal, but it would clearly be immoral).
I can probably look it up but I received a not inconsiderable sum of money for my shares when I sold them many years later. I presume my parents sold and spent the money very soon after the plan went through. All members received shares (it would be obviously inequitable to propose that only those voting for the deal get shares if the vote passes, I'm not sure if that would be straight up illegal, but it would clearly be immoral).