The situation is quite different under a strict liability rule. In this case, firms are liable for all harm that workers incur in the workplace. But if firms cannot observe workers' care levels, then the previous reasoning breaks down.
To see this, suppose that firms choose the efficient level of care, and that they want to induce workers to also choose x*, the workers' efficient level of care. Note that under a strict liability rule, firms certainly have an incentive to try to do: under a strict liability rule it is firms that bear the costs of harm to workers if an accident occurs.
Suppose that firms offer workers a wage of
As much as firms would like it to be the case, this will simply not induce workers to choose the efficient level of care. The reason is straightforward: worker care is unobservable and non-contractible, and so a rational worker will simply pocket the wage in (6.28) and supply no care, so xv = 0. This happens because workers are compensated for all harm under a strict liability rule - there is no benefit to the worker taking any care, even if they are paid to do so.
Hence, under a rule of strict liability, firms will offer a wage of m, and will incur total costs of
This is the unique competitive equilibrium here, and so the rule of strict liability is not efficient.