What you’re describing is the difference between positive and negative liberty. In the case of healthcare, negative liberty would be one’s freedom from having to pay taxes to support the healthcare of others, positive liberty would be one’s freedom to get equal and fair access to healthcare. Libertarianism does concern itself more with the idea of negative liberty, as it seeks to separate from the state’s interference in the lives of the individual.
Libertarians: maximum freedom for everyone!
Everyone: what about healthcare?
Libertarians: you’re free to die in a gutter!
What you’re describing is the difference between positive and negative liberty. In the case of healthcare, negative liberty would be one’s freedom from having to pay taxes to support the healthcare of others, positive liberty would be one’s freedom to get equal and fair access to healthcare. Libertarianism does concern itself more with the idea of negative liberty, as it seeks to separate from the state’s interference in the lives of the individual.