The Seventh Circuit, interpreting Illinois law, has even held that the mere promise to relocate is sufficient to estop the employer from revoking his promise to employ. See Gould v. Artisoft, Inc., 1 F.3d 544, 549 (7th Cir.1993). A promise in exchange for a promise is sufficient for the formation of a contract, and each promise binds the parties to their agreement. Id. at 550. In Gould, a promise to relocate was binding enough to have detrimentally changed the position of the employee, and thus the employer was estopped from altering the contract. Id.
Under this law you may have an argument that the employer has a duty to pay you for salary that you would have earned for a reasonable time of employment [to be determined by a jury considering all the facts] or to pay you for your relocation costs.
If you want to sue for mental anxiety damages, you may have to prove up elements of intentional or negligent infliction of emotional distress. See this link. This is not easy in the context of employment cases.
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