Does the IRS catch a mistake if 2 people claim the same dependents before refund is issued?

If both people file their returns electronically the answer is yes. Once a social security number is used electronically, it cannot be used a second time. If one or both of the returns are filed by mail, refunds may be issued but at some point letters will be sent to both people claiming the dependent and they will have to submit proof that they have a right to claim them. Proof will be required for the three tests to prove you can claim the person. For Earned Income Credit, the tests are Relationship (must be your child, brother, sister, or descendent of these.