Section 133 (1)(K) of the Immigration and Refugee Protection Regulations says she is NOT eligible to be a sponsor if she goes on welfare before a FINAL decision is made on the application.
http://laws-lois.justice.gc.ca/eng/regulations/SOR-2002-227/page-67.html133. (1) A sponsorship application shall only be approved by an officer if,
on the day on which the application was filed and from that day until the day a decision is made with respect to the application, there is evidence that the sponsor....
(k) is not in receipt of social assistance for a reason other than disability.
This looks like it implies that since the sponsorship part of the application has been approved that she is home free. But that's not what it means. It means the day in which a decision is made on the application for PR of the person she sponsored. If a VO assessing the PR application looks for current verification of her income and finds out she is on welfare, the sponsorship eligibility will be revoked and PR application refused. There is a chance that they may not look. But if they do...
Section 39 of IRPA must also be satisfied:
39. A foreign national is inadmissible for financial reasons if they are or will be unable or unwilling to support themself or any other person who is dependent on them, and have not satisfied an officer that adequate arrangements for care and support, other than those that involve social assistance, have been made.
If her income is already low, they WILL look at their ability to be self-sufficient when/if the spouse is awarded the PR visa. They can/will look at his ability to find a job in Canada and earn an income to contribute to the support of his family. There have been a few cases refused based on this even when sponsorship has been approved.
Nobody is questioning her eligibility or need for social assistance. She CAN apply for it and receive it. But the law says that she is NOT eligible to be a sponsor if she is in receipt of it (other than for disability) for the DURATION of the processing of the application. This law came into effect in 2002.
It may be harsh and unfair and I wouldn't suggest she starve either!!! Of course not! But the reality is that it's a matter of priorities. It may be in her best interests to withdraw the sponsorship and wait to apply again when she is back on her feet.