The stub should be be 'capped', (covered-over might be a better term) to stop any harmful dirt/debris from entering, but it must NOT be closed-off completely, otherwise any oil vapour/excess pressure that should be escaping the crankcase/transmission housing would not be able to do so, possibly causing a vacuum and even leading to expensive trouble.
Although a very simple device, it does both these things in one unit, that's why 'breather filter' is an apt description.
Incidently, a breather fitted to an engine cranckcase/cylinder head/cam cover used to let oil vapour escape does eventually get clogged-up with oil, (sometimes quite quickly if the engine is well worn) so it has to be replaced before it gets so choked that it can't 'breath' any more. The one on my Daihatsu camcover lasts about a year/13,000 miles before it gets too gooey and needs replacing.
Technicaly, the car isn't 'Type Approval' legal anymore, in that part of the emmision-control systems on the car has been by-passed/disabled
- oil vapour that 'should' be re-circulated through the inlet system is now being vented to the atmosphere, (Greenpeace would'nt like it, lol) - but it's no different to how all cars used to be not so many years ago. Like other similar mods, (de-cat pipes, over-size thottle bodies, e.t.c.) it's upto an individual's conceince.