Under normal circumstances, a U.S. citizen or lawful permanent resident who is petitioning for a family member to receive a U.S. green card (lawful permanent residence) must agree to support that person -- and be able to show income and assets worth at least 125% of the U.S. government's Poverty Guidelines levels. (For details on reaching these levels, see "How Much Income an Immigrant's Sponsor Needs to Show According to the Poverty Guidelines.")
However, there are (admittedly rare) circumstances under which either the U.S. consulate or U.S. Citizenship and Immigration Services (USCIS) -- whichever of these is handling the immigrant's application for an immigrant visa or green card -- may ask the sponsor to show earnings or assets of even more than the government’s minimum requirements.
In viewing the personal or health situation of particular immigrants, USCIS or the consulate may decide that an immigrant presents an unusually great risk of becoming a "public charge" -- that being a ground of inadmissibility in which the person is likely to have to rely on need-based assistance from government agencies in the United States. Elderly applicants and those with severe health problems that might prevent them from working or result in large medical bills fall into this group.
The consulate or USCIS may learn of significant health problems through the medical exam that is a required part of your application.
Finding additional sponsors might be enough to help you overcome these added requirements.
It is hard to predict when or whether the government will ask the sponsor for an unusually high level of proven income and assets. The request probably won't be made until the immigrant is in the visa or green card interview. In the case of the visa interview, the U.S. sponsor is unlikely to be present.
Don't worry that being unable to come up with more sources of financial support on the spot will result in the visa or green card instantly being denied. The immigration officials always give applicants more time to provide new or further evidence before making a decision. But there are a couple of advantages to advance planning if you know that your case is a marginal one.
One advantage, of course, is that having extra documents or affidavits on hand may shorten the time before the case is approved. Another is that cases that aren’t approved at the visa or green card interview tend to get greater scrutiny when they are later evaluated by the interviewers and their supervisors. If you are understandably reluctant to turn in an extra Affidavit of Support from a joint sponsor, the immigrant can always keep it in his or her back pocket and give it to the interviewer only if he or she says that more sources of financial support are required in order to approve the case.