You can only make a claim like that if you can prove real damages. The idea is that someone made you a promise, and based on that promise you took steps that cost you real money. Maybe you quit your job. Or you paid to move cities and all the related costs.

So the employer would have to prove they suffered real damages as a direct results of the employee backing out. And that would be difficult in most cases. After all, in most cases the result of an employee backing out will just be the status quo the company was already operating under. And they would have to show why they couldn't just go with another candidate.

It would be a lot harder for an employer to make this kind of claim than an employee. Sure you can imagine some edge cases where a company spent a lot of money in expectation of a new employee. But usually a new employee backing out just means the company keeps operating in the exact same state it was previously.