Applicants for an immigrant visa in the United States usually require a sponsor. This sponsor can be a relative--either a spouse, parent or child--or an employer. Family members must either be U.S. citizens or have permanent resident status (a "green card") and be able to support the immigrant enough to prevent them becoming a financial burden on the state. Employers must provide a job for the immigrant that cannot be filled by a current U.S. citizen or green-card holder. Because sponsorship is legally binding once issued, it is very difficult for sponsors to revoke it.
If the application for sponsorship has not been filed or is still pending, petition to have it withdrawn. This can be done by either visiting the nearest U.S. Citizenship and Immigration Services (USCIS) office or by notifying the agency in writing of your wish to withdraw your sponsorship. However, you cannot petition for revocation after the application has been approved and the visa issued.
If the visa has been issued, do not attempt to violate your sponsorship agreement. The form used to sponsor an immigrant, USCIS Form I-864, an affidavit pledging support for the immigrant, is legally binding. A sponsor who violates the agreement can be sued for damages by the immigrant and by any agency that provides the immigrant benefits.
If possible, get the immigrant to agree to a revocation of sponsorship. Although you cannot arbitrarily revoke your sponsorship, if both the sponsor and the sponsored immigrant agree to have the sponsorship canceled, they can offer a written request to the USCIS, who will, in almost all cases, agree to the petition. This may be unlikely, however, as immigrants rarely voluntarily relinquish hard-to-obtain sponsorships.
While you cannot revoke your sponsorship on your own, if the sponsored immigrant has violated the terms of the I-864 or acquired it under false pretenses, notify the USCIS. If the USCIS rules that the immigrant has committed an infraction serious enough to lose their permanent resident status, your sponsorship of the immigrant will be nullified. For instance, if you are an employer and the employee refuses to work, this could qualify as fraud, which the USCIS would interpret as an abrogation of the sponsorship contract. Likewise, if the immigrant petitioned for immigration without noting a previous criminal record, this would also likely cause them to lose their status.