It sounds to me like this person is asking you to act as a sponsor for their I-864, Affidavit of Support, which is a quite serous request to consider.
As a sponsor, you are responsible for re-paying any means tested public benefits that the intending immigrant incurs, just as the US citizen spouse would be (you are co/joint sponsors of the intending immigrant), but does not repay himself/herself. Basically, you are making a contract with the US government that if the intending immigrant makes use of any of the following public benefits, you will be the responsible party for repaying the costs:
- Food stamps
- Supplemental Security Income (SSI)
- Temporary Assistance for Needy Families (TANF)
- State Child Health Insurance Program (CHIP)
This responsibility remains your for at least 10 years, and it can only be terminated in the following ways:
- intending immigrant becomes a US citizen
- intending immigrant/you die
- intending immigrant is deported or otherwise departs and abandons lawful permanent resident status
- has worked or can be credited with at least 40 hours of work under the Social Security Act
Again, this is a serious matter to consider, as it may have consequences upon you, if things go wrong. Also remember that even if there is a divorce between the parties, you are still on the hook for the sponsorship.
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