Meggsy you are incorrect on what happens when someones EI runs out.

The reason Unemployment stats look the same is that if you are not either working or looking for word you are not part of the labour force.  The all time hi in the Labour Force Participation rate for Canada was 67.70 which we hit in Sept 2003, currently is 65.6% (they count those 15 and older)

The unemployment rate is the difference between the labour force and the number of employed persons.  To see what I call the shadow unemployment rate you just need to look for an decrease in the labour force participation rate.  For example if the participation rate falls 1% but the unemployment rate stays the same then an additional 1% could be added to the UI Rate if you wanted to count those discouraged workers.

Also just because EI runs out does not mean people become homeless - there are other assistance programs you can draw on or they might not be the only wageearner.