What is the name of your state? NJ
Hello: a close friend of mine is filing for her premanent residency under condition of marriage to US citizen. Her husband's income is not enough so they need a co-sponsor. I really like to help her but what would be responsibility if I co-sign for her? Will I be financially responsible if she files for unemployment while she is not a premanent resident?
That's nice for you to help your friends!
It is a serious commitment, but if you know your friend well you will know if you should be concerned or not.
The I-864 (the Affidavit of Support they need you to complete) is meant to reimburse (pay back) for any "mean tested benefits" she applies for AND receives. You can google "means tested benefits" to find the list, but it is primarily what we call 'welfare" and medicaid.
Unemployment is an employer funded insurance policy run by each State, and it is not a means-tested benefit.
However, if your friend got ill and they didn't have insurance, IF she claimed poverty benefits and treatment, you might be asked to repay amounts they gave her. It's important to remember that most of these benefits are not available to new immigrants for their first 5 years in the US.
You might ask her to place some conditions on your support. Maybe ask her about getting pregnant, and if they plan to wait to have a family etc. I know that is very personal, but having a baby is expensive and people don't always think carefully.
You could do what I did. I told my husband that part of the Joint Sponsor deal was that he would need to become a US citizen as soon as he was eligible (3 years after immigrating). He did, and now there is no I-864 at all.