Form I-1864A, issued by U.S. Citizenship and Immigration Services (USCIS) is used in one narrow situation: where a U.S. citizen or permanent resident petitioning for an immigrant does not have enough income or assets to sponsor that person alone.
Realize that no matter what, the main petitioner will have to prepare and sign an I-864 Affidavit of Support promising to reimburse any U.S. agencies to which the immigrant later turns for need-based financial and related support. But additional support might be needed.
By signing an I-864A, a household member or dependent can make their income available to the main sponsor as well, so as to promise full support to the intending immigrant and help that person successfully get a U.S. immigrant visa and permanent residence (a green card).
Form I-864A is a contract between the U.S. sponsor and the family member living in the same household or among the main sponsor's dependents, and an attachment to the primary affidavit used by family immigrants, USCIS Form I-864.
As an example of when Form I-864A might be used, let's say the main U.S. petitioner of the immigrant is a 40-year old woman who is sponsoring her foreign-born husband (based on their marriage). Her 20-year old daughter lives in her house and has a regular job. If the mother-sponsor's income is insufficient to satisfy U.S. immigration regulations by reaching 125% (in most cases) of the Poverty Guidelines, the daughter could sign an Affidavit of Support to help her mother sponsor the immigrant.
This is no small favor. The household member joins the sponsor in being liable to the U.S. government under the original Affidavit of Support.
In literal terms, this means that both the sponsor and the household member agree to reimburse any government agencies who provide the immigrant with need-based financial assistance within a certain number of years. The liability is "joint and several." That's legal language meaning they don't just split their obligations down the middle. Instead, either person can be held responsible for the whole amount owed, if need be.
A mere roommate cannot sign an I-864A. This obligation can be undertaken only by an actual relative of the petitioner (spouse, adult child, parent, or sibling), who is living in the same principal residence. Or, even if not living in the same house, a relative or other person whom the sponsor has lawfully claimed as a dependent on their most recent federal return can sign Form I-864A.
Not all household members will be willing to sign onto such an obligation. But in one important situation, it is in their own interest. The intending immigrant, if living in the U.S. already, can, in certain circumstances use their own income to sign onto Form I-864A, as described next.
The intending immigrant can be a household member if either married to or living in the same principal residence as the sponsor and able to show a source of income that will continue even after becoming a green card holder. (This requirement can be a problem for immigrants who are currently working without legal authorization.) The green-card applicant can then sign Form I-864A; but doesn't need to unless children (dependents) are also immigrating.
Note also that, in some cases where an immigrating spouse or other relation already lives in the U.S., the petitioner need not fill out Form I-864 in the first place. This is true when the immigrant has already earned (or can be credited with) 40 quarters of Social Security coverage. That usually means having worked in the U.S. for approximately ten years, having been married to someone who did so, or having been the child under 18 of someone who did so. In such a case, the immigrant would need to fill out Form I-864W to claim the exemption.
For more on the Affidavit of Support requirements, see Financial Support You'll Need to Apply For a Family-Based Green Card.