The employers could instead ask "what do you think the percentage of employees who have stolen from their job is?" and know that the applicants who responded higher than average were correspondingly more likely to steal, and the applicants who responded lower than average were less likely to cheat. It could cut through all sorts of social desirability distortion effects.

1. The method will work until it becomes broadly applied and thus well known. After that the correlation would disappear. (Related to Goodhart's law.)
2. In the meantime, the group who profits are not the non-thieves in general, but the non-thieves who are most biased in the typical mind fallacy direction. I disapprove of methods which reward bias.
3. The method itself is dishonest communication. Universally applied it would be a Nash equilibrium (at least until Goodhart's law strikes back) since each employer individually is better off applying the method, but dishonest communication is less effective and thus the situation would be Pareto suboptimal.

Obviously, none of the above means that your suggested method doesn't work, but nevertheless I wish people don't use it.

You couldn't get the exact likelihood, but it would give more useful information than you would get with a direct question.

What do you mean by "the exact likelihood"?