Those sponsorship programs are geared specifically towards Nationals only. You will find in the case of CX, that cadetships are offered only to Chinese nationals or HK resident card holders - same applies to all, and there's not a huge amount, other carriers. Since most flagships who offer these programs are partly or with a majority of funding provided by the government, there would be very few - if any - situations where you'd find a gov't paying for flight training or approving their flag carrier to pay for a foreigner to be a qualified pilot for their airline.
I see you're from Canada, as am I, and I am sure you would agree that you'd be a little pissed to learn that Air Canada was paying for foreigners to learn how to fly for their airline. As for Europe, there may be some quietly known sponsorship programs however, these will be geared towards 18-21 year olds, straight out of their A levels/ GCSE or highschool and would involve a very lengthy pscychological and psychometric testing.
It seems these days that the only way of pursuing and achieving a successful flying career is a bunch of money and a little bit of luck regardless of surplus or shortage.
yyzdub