In extenuating circumstances some members have been enrolled with PR status. However, in 2014 I do believe there were approximately 60 members with pr status in the entire CF.
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DAOD 5002-1 Enrollment Part 3
3.3 An applicant is required to be:
a Canadian citizen; or
a citizen of another country who has permanent resident status under the Immigration and Refugee Protection Act and:
undertakes to become a Canadian citizen immediately when eligible to do so;
provides service that satisfies a special need; and
whose enrolment, in the opinion of the Commander (Comd) Canadian Forces Recruiting Group (CFRG), would not prejudice the national interest.
One issue is that a person must maintain permanent resident status. PR Status may be lost if a refugee returns to visit their home country (demonstrating they no longer require protection) or apply for a passport from their home country. Permanent Residents must be physically present for two years within five years on the day the determination is made. The residency requirement for citizenship is a fixed period in Bill C-24 currently six years previous to day of application in Bill C-6 the act about to come into force its 3 years in the five year period previous to the day of application. I have sworn serving members of the CF as Canadian citizens.