Wrong...sponsor is responsible indefinitely....this 10 year thing I see on here all the time is just wrong. It is only 10 years if they are working a job to earn the needed SSA credits, or they become a citizen. Other than that, the sponsor is on the hook.
From my I-864:
When Will These Obligations End? Your obligations under a Form I-864 that you signed will end if the person who becomes a lawful permanent resident based on that affidavit:
A. Becomes a U.S. citizen;
B. Has worked, or can receive credit for, 40 quarters of coverage under the Social Security Act;
C. No longer has lawful permanent resident has departed the United States;
D. Is subject to removal, but applies for and obtains, in removal proceedings, a new grant of adjustment of status, based on a new affidavit of support, if one is required; or
E. Dies.