The way it could work in that particular situation is that when somebody opens an EI claim, typically it would be open for a 52-week period. If the only thing they're claiming during that time is the sickness benefit—it gets very complicated if there are multiple types of claims—they can claim those 15 weeks over that 52-week or one-year period. They have flexibility in terms of the weeks during which they may claim those benefits, but they must take them in units of one week.
In order to open a new employment insurance claim after that, they would have to have worked a total of 600 hours.