Interesting idea, but if you need medicine for your child and are low on cash, you will sell those stocks today rather than save them for the future.
And the buyer will be someone who has enough cash to not worry, and will thus get even more cash to not worry.
That is, I don't think it'll be that simple.
edit: one way to solve the above would be like the Spanish coops, where the ownership (stock) is tied to your employment. IIRC you have to buy say one stock to get employed, and you can only sell when you leave your position.
But then it's harder to redistribute the stocks...