Here in Nova Scotia, you have to actually be on welfare to qualify for something like that, being on EI wouldnt make a difference.
Things are different in NS, we have MSI, covered medical care...to a point. You pretty much just have to be a legal Canadian citizen http://www.gov.ns.ca/health/msi/ and BC http://www.health.gov.bc.ca/msp/infoben/premium.html . BC has a totally different set up. Under MSI, there is no charge to a patient (normally) for a doctors office visit. But, there are charges if you dont show up for your appointment and there is often a charge for medical notes for absences for work.
I'm not sure what the rest of your medical is like ie: prescription medications. Here it's full price if you don't have some sort of medical plan through a workplace or on your own. We would be in pretty bad shape if we had to pay full price for it all; my husband is a heart patient and I have arthritis in my neck and back that I have to take meds for; were grateful he has a career with decent medical/dental/pension at a decent premium cost. Required surgeries are covered here, cosmetics ones are not. Our dental and glasses are not 100% covered but the costs are a lot less with coverage. Children have basic dental coverage under MSI until they are 10 yrs old then they fall under health coverage if one has it.
I find it interesting that there is such a difference between our two health care systems. I figured most provinces were the same as NS with an MSI type health care; I was mistaken.