Daniel Kuehn and Hazel Meade pretty straightforwardly state my objection. I think I'd just reiterate that the problem comes when the equilibrium wage is sufficiently low that the optimal trade off David suggests would seem to no longer work. Suppose the cost of safety is $0.25 a day and the employees value it at $0.50 a day. So it seems like a trade is in the offing, except suppose the going wage is only the $2.00/day that supposedly constitutes a basic subsistence wage in the poorer parts of the world.
At less than $2.00 a day, we can say the employee starves. So the worker won't seek this safety and the employee won't grant it. Because a probability of getting hurt is a better risk than a certainty of starving.
Here's the problem with MikeDC's reasoning. If at less than $2.00 a day the employee starves, then he is right that the employee will not seek this additional safety. But then he should question his assumption that employees value the additional safety at $0.50 per day.