I was given a date by which I have to leave Canada but my medical condition prevents me from traveling, can I stay in Canada?
There are ways to defer your deportation pending a particular outcome. Your lawyer can write a carefully drafted letter with documents and evidence to Canadian Border Services Agency (CBSA) explaining your circumstances and requesting them to defer your removal until your health issues are resolved or another solution is reached. This is called a Request for Deferral. Your lawyer may advise you to make an application for status in Canada under an existing category that might apply to you because an outstanding application to CIC can weigh in favor of a deferral.
If a deferral request is refused, you can apply for a Judicial Review of the deferral refusal at the Federal Court. Your lawyer will represent your case at the Federal Court and make arguments about why the decision to refuse a deferral was wrong in your particular circumstances, given the evidence CBSA had in front of them.
Both a Deferral Request and a Judicial Review are complicated matters demanding high levels of skills, legal knowledge, and experience of dealing with similar cases.