But the Fiji Indian Association called it "heartless".
Mrs Begam's daughter, Fozia Ali, said the family was "very scared and disturbed by Sanil Kumar's case, as we don't want her to go through the same ordeal".
"We know the end will come soon. She's in a lot of pain. Her bones are very soft, and she has very limited mobility.
"She has nothing at all in Fiji. No one to go to."
In a letter to Prime Minister John Key, Ms Ali wrote: "We are a close-knit family, but I can't accompany my mum to Fiji as I have four children aged 9, 7, 5 and 3, and my brother Shakeel has two kids, aged 4 and 2.
"Sending her to Fiji would mean dying alone and away from family without peace, love and family support ... leaving her to die without her kids, husband and grand kids. This issue leaves me heart broken."
Mrs Begam has been in New Zealand for six years and was diagnosed with cancer in 2011. She has twice been declined residency, and in February this year was denied a work visa because she did not meet health standards.
In declining the work visa, Immigration NZ said: "There is a strong case that the client can receive all the relevant care that she needs in Fiji and at a lower cost to the client and her family."
The Auckland DHB had been treating Mrs Begam, but it had stopped treatment when her work visa was declined.
DHB director of the cancer and blood directorate, Richard Sullivan, said he sympathised with her situation.
"But Auckland DHB does not have discretion to treat people who are ineligible for free public healthcare."
The family says they are paying off a debt to the DHB of about $16,000 -- but the DHB was unable to confirm this.
The Prime Minister's office has referred the matter to Ms Kaye, who expected to make a decision within a week.
Ms Kaye did not want to comment on the case, but said that one factor she considers is the effect on New Zealanders' access to health services.
"In terms of my decisions ... some of them involve consideration of a range of factors including access to treatment for New Zealanders.
"Some of those decisions include enabling people with significant illnesses to remain in New Zealand."