If they enter the dependents on their tax return and try to e-file the return it will be rejected by the IRS.
If they print and mail their return with the dependents, the IRS will pay any refund based on the dependents.
However, since the IRS received two separate returns with the same dependents entered, the IRS will investigate. Within a year you and the other party will communications in the mail from the IRS investigating this situation. The loser of the investigation has to pay back any refund based on the dependents plus penalties and interest.
