Actually, it is possible. Not easy, but here's how it works.
A common-law partner is defined as "common-law partner means, in relation to a person, an individual who is cohabiting with the person in a conjugal relationship, having so cohabited for a period of at least one year. (conjoint de fait)"
So you haven't cohabited. However, you may qualify as a conjugal partner
"
Interpretation — common-law partner
(2) For the purposes of the Act and these Regulations, an individual who has
been in a conjugal relationship with a person for at least one year but is
unable to cohabit with the person, due to persecution or any form of penal control, shall be considered a common-law partner of the person."
These are the from the Regulations that govern Immigration to Canada. ->
https://laws-lois.justice.gc.ca/eng/regulations/SOR-2002-227/page-1.html#h-2
Practically speaking, you will need to talk to an experienced immigration attorney/consultant to understand how you can prove that you have been in a conjugal relationship for at least one year, but were not able to cohabit due to fear of persecution. This is way out of the scope of this forum.
Just know that it is possible in theory, whether or not you can prove it in your specific case is a different matter.