Fugitives on the run and wanted for some of the most serious crimes and sexual offences could soon be stripped of their welfare payments.

Labor quietly tacked on an amendment to a separate social security bill last week, weeks after the proposed changes were examined by a Senate committee.

The bill intends to deliver compensation to people slapped with unlawful welfare debts, but the new amendment would also grant the minister power to stop welfare payments for people "subject to outstanding arrest warrants for serious offences".

The changes would apply to social security payments and concession cards, family assistance payments and paid parental leave.

The amendment does not apply to childcare subsidies. Family tax benefits can be transferred to another eligible guardian.

It has been

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