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When they government finds out your wife is on welfare and you are paying no child support or alimony, then they will suit you for payback of the welfare she received since you have primary duty to provide child support.
What if the child is receiving K-TAP (welfare)?
If a child is receiving K-TAP benefits, the Commonwealth of Kentucky will bring a child support action against the non-custodial parent(s) to obtain re-payment for the state’s support of the child. The local Child Support Enforcement office will contact the child’s custodian to get the name and address of the non-custodial parent(s). Refusal to provide this information about parent(s), or providing false information, is a crime. KRS 205.785.
kyjustice.org/node/606