If the standard breathers are working correctly it SHOULD cut out. If they are blocked then it won't cut out or will run lumpy. The reason is the fuel metering unit draws on the breathers and it meters this air. When you take the cap of, you introduce unmetered air into the induction system which also drops the amount of vacuum and causes it to run too lean for it to stay running.

A poorl sealed dipstick or gaskets on the engine can also effect the way the engine runs.

My car has had the breathers removed from the induction system completely and have blocked the port of in the the meter unit and the car set up accordingly. The breathers than go to a breather oil seperator and then to atmoshpere (a catch tank could also be used but it still ultimately breathes to atmosphere).