I wish you would define your terms. Line training...what does that mean?
In the US, we have something called: LOFT or Line Oriented Flight Training. 20 year veterans still take this training. Its just a regular flight in real time with a minor problem thrown in for good measure.
Do you refer to people paying to be a copilot, after passing some simulator check ride? Just to build time?
That sort of thing is not done at major airlines in the US. There are regional airlines that have hired very low time pilots to be copilots, but they are still being paid...albeit not much.
A few years ago I had heard that some of the cruise ship airlines had unpaid copilots.
The only way to stop something like this is to expose it to the light of day.
Dear Passenger, do you want your flight crew to have to have training wheels?