Am I eligible for employment insurance if I am placed on leave without pay?

If employees are on leave without pay for a period of 5 days or longer, they will be temporarily struck off strength in the pay system and they will be issued a record of employment.  The rules governing eligibility to EI are available here: https://www.canada.ca/en/employment-social-development/programs/ei/ei-list/reports/digest/chapter-6/periods-of-leave.html