Left-Libertarian, would be a solid way to describe my own politics I believe. I prefer Liberal or even Classical Liberal, Social Liberal even, but I'm someone whose all about individual freedom. But that it should be for everyone. That everyone should have the opportunity to achieve that and not have to live off any welfare state or private charity if just given the opportunity to live freely. And that is where government has a role. Not as the director of society, but as a supporter and even referee. Not to call the plays and coach the teams, but to step in when predators break the rules that hurt the innocent. So that is where I guess Left-Libertarians, or Social-Liberals and Liberals, disagree with the Ron Paul Classical Libertarians lets say. Who just want government to stay home and perhaps arrest people when take from someone else's freedom. Or stop invaders when they invade the country.
The Left-Libertarian argument for the welfare state or what I prefer is the safety net, is that poverty is a real threat against freedom. And it keeps people down trapped away from freedom. So what you can do with a social insurance system is to help those people in the short-term and prevent them from having to deal with the worst forms of poverty like homelessness. As well as help them get on their feet and live in freedom and not off of taxpayers. Which promotes freedom and for everyone else, because you're creating new taxpayers and real consumers with real resources to consume the products that are made by the private market. Which creates good jobs for everyone involved. Not an argument for a big centralized superstate where states and localities become almost non-relevant, or high taxes across the board. That discourages individual freedom and individualism. Just an insurance system for people who truly need it to help them achieve freedom as well.