If I'm not eligible for an open work permit while applying for PR outside of Canada, then how do I legally stay living and working in Canada while the PR is being processed?
As the other poster said, you can apply for a change of conditions to your current status from worker to visitor. But you cannot work as a visitor. However, if your employer wants to keep you, they must apply to Service Canada for a Labour Market Opinion to be allowed to hire a foreign worker. They must meet the advertising requirements for the skill level of the position, prevailing wage and show that no Canadian or permanent resident that applied for the job was qualified and/or willing to take it. If they receive a positive response to their application, you can obtain another work permit.