Yes, if you file your taxes and your dependent has been claimed by someone else already, then you would receive an error message about the dependent's social security number matching a social security number filed on another tax return.
If your dependent was claimed when they should not have been, you can ask the other party to amend the return. If they will not remove the dependent, you may file on paper. The IRS will contact both parties to determine who is entitled to claim the dependents, and will credit the person that met the requirements. If it is determined that the other party should not have claimed the dependent, the IRS will make them pay back the exemption along with any penalties or interest associated with their false claim.
