[defen]

It's possible that he perceived his ownership stake as having negative value - e.g. due to tax reasons or other regulatory overhead (needing to participate in board meetings or whatever), legal risk (they get sued for doing something desperate and dumb and he needs to participate in the lawsuit) etc. But you can't just dissolve your shares, you have to either shut the company down entirely or sell your stake to someone. If he thought the company was truly worthless / negative expected value then $100 is fair consideration.

A famous example of this is Ronald Wayne selling his 10% stake in Apple for $800 because he was worried that Jobs would incur a bunch of risky debt that he'd be liable for.

[chii]

i would've imagined that a limited liability corporation means that the lowest value it can go is zero, not negative.

A shareholder cannot and should not ever be responsible for the debts of the company imho. As for time costs, the shareholder could just not attend or do anything, if they perceive the work to be of worthless value, and thus, should therefore have zero as the floor, rather than negative!