I do not believe that there is any visa status that would meet your goal of having your sister remain in the US until her final days. Even if you are a US citizen and petition for her, the period of time for her to immigrate is is approximately 10 years, and during that period, U.S.C.I S. will not allow her to stay legally. Perhaps if your sister's end is soon approaching, the agency may be sympathetic and allow her extensions of her visiting visa, but if she is in fairly good health with no immediate end in sight, there would not appear to be anything within the law to allow her to stay until her final days.
If she is too ill to travel, that would be the only way to allow her to stay here after her vistor status expires. You could petition for her to immigrate if you are a US citizen, but it takes about 10 years for a visa number to become available for this familiy category.
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