The first question on the Application to Sponsor and Undertaking form asks:
1) If you are found ineligible to sponsor, indicate whether you want
To withdraw your sponsorship. All processing fees less $75 will be repaid.
To proceed with the application for permanent residence.
In order to understand what this question is about, it is important to review the steps to bringing a family member to Canada.
The first is to successfully apply to sponsor the family member. This costs $75 in processing fees. Reasons that a sponsorship application will be rejected include criminality, failure to meet the minimum income cutoff, and other eligibility requirements. The second step is for the foreign national to successfully apply to immigrate as a member of the family class. This costs $475 for the principal applicant, plus an additional $150-$550 for additional, accompanying, family members. Once you start a step, these processing fees are non-refundable.
If your application to sponsor has been rejected, then the applications for permanent residence will also fail unless there are sufficient H&C grounds. Citizenship and Immigration Canada thus provides you the opportunity to withdraw before the applications are processed. If you withdraw, you will not have to pay the processing fees for the application for permanent residence.
However, if you do withdraw, then you will lose your right of appeal.
As such, there is a fair amount of consideration that should go into answering this question. If you are found ineligible to sponsor, do you want to appeal? Are you prepared to pay the extra expenses that will come with processing the application for permanent residence and the appeal? Would it be simpler to start over? Which will be faster? What is the likelihood of success on an appeal?
These are all questions that you need to discuss with your representative before answering this question.