That's a difficult question to answer but based on what BCPNP and IRCC informed me, the PR process still continues as the applicant searches for another job. However, if the nomination is employer restricted and the applicant is terminated with cause, IRCC conducts its investigation which affects the PR process. On the contrary, if the applicant was terminated without cause, the PR process continues. Also take note this was last year and with the Pandemic, there was a level of flexibility from both authorities. Back to what I said earlier, communication. You just may never know what their reaction will be. When I contacted BCPNP to explain my situation, they were surprisingly very understanding.
I get your question, what happens in that window between unemployment/self employment and completion of the PR process. How about shooting BCPNP an email with a hypothetical question, on what happens if an applicant voluntarily leaves their job due to ????