They're called social democrats or socialists in Europe and liberals in the United States. They're no fan of the free market, they want to protect the poor and huddled masses against the sharp edges of capitalism. Then there are the people that are called liberals in Europe and Republicans in America. They want to free the economy from red tape so that entrepreneurs can do their thing and everybody wins, even the poor. Neither group is helping the most vulnerable people in society.
The protections offered by the social democrats don't really help the poorer people. Mostly they create systems that are too complex and only help bureaucrats and smart people. On top of this, they usually treat the people they are supposed to help as too stupid to decide what is good for themselves. The parties that officially support the free market are mostly for free markets as long as it is good for the companies. Real competitions would only erode the possibilities of profits. They'd rather spend as little as possible on social security, so fixing usually means cutting down.
Giving subsidies to the poor so that they can do stuff they cannot affort seems nice, but it means that the government decides that the poor can now spend money on going to the opera instead of on shoes for their kids. Because the government knows what is important and the poor don't. Cutting all subsidies doesn't really help the poor either. Cut the subsidies and give the money to the people. People are smart enough to make this kind of decisions, or at least smarter than the government.