Does such thing exist? I was laid off my 40 hr/week job due to a shortage of work. I however have had a second job working at a bar on the weekends. A girl I worked with said there is partial EI. Couldn't find anything on Google, but there is a fair bit to read threw.
My understanding of EI is that you can file a claim right away with your ROE from the job you were let go from.
You have to report your income to EI though and they will claw back some of the money, 50% I think, on any earned income. It is definitely worth a trip to EI to find out.
I don't know how they do it now but one of the questions I'd fill out every week was something like this;
Did you start a permanent full time job?
I'd answer no even if I was working full time as it wasn't permanent on construction where lay offs happen pretty regularly. Some jobs last a year, some only a week. This way I could collect EI without the two week wait if I got laid off or if I didn't work that week I'd get a check. Just report your earnings and days worked and you should be good.