When an individual submits a green card application to USCIS, they also certify that all the information listed on the forms is complete, true, and accurate under penalty of perjury. If you would like to include the insurance information on the forms, the information provided must be accurate and current, so the health insurance would need to be current at the time of filing.
Generally speaking, the applicant should have health insurance coverage from the time the application is submitted through to their green card interview. If their health insurance coverage expires, they can bring updated health insurance information to the green card interview.
For more information regarding supporting documents required under the public charge rule, go here.
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