When you say, "would they know," do you mean the Department of Revenue? Almost certainly not. Do you mean the other parent's attorney? That's possible.
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If the custodial parent knows you had an accident, and mentions it to a private lawyer, or department of revenue or the state attorney- whoever handles the enforcement, they can obtain a lien on it before its disbursed- and at that point your lawyer cannot release the money once on notice of lien or intent to seize. Further, if your ex finds out after you get the check, the department can freeze and/or intercept the money in your account, with the exception being certain joint accounts. Be mindful of this. Otherwise there shouldn't be a problem at least in getting the check.