EI is not welfare. It's an insurance plan that you, as a worker, have paid into. You're entitled to it* and it will not jeopardize your PR status, not will your wife have to pay it back.
1. EI is an insurance scheme, you pay in while you work, and collect when you are unemployed, it is not public assistance.
2. Whether you can collect or not depends on how many hours you have worked. See:http://www.servicecanada.gc.ca/eng/ei/types/regular.shtml