I won't debate the rest of what you think but what you said in the quote above is not likely. First, it's not a medical program, it's a unique medical service that the recipient MUST legally apply for and be legally approved for.
Secondly, no government medical service or any other kind of service provider or even a friend or family member in Canada can suggest to anybody that it is better for them to consider being euthanized. Not even as a joke.
It's illegal, a criminal act, to make such a suggestion (it's called criminal coercion) and anyone making such a coercive suggestion to ANYBODY can and will be charged, and sued / convicted to the fullest extent of the law.
I think somebody has been pulling your leg and taking advantage of your own suggestibility. You might want to check the credibility of the source that you got that information from because it is "dead" wrong. Pardon the pun. If the mil said to somebody else that some government program told her it would be better to get euthanized then that mil should report them to the police and file charges against them and sue the pants off them.