A rising tide lifts all ships…
Being dependent is not at all a good position to be in regardless of the system. The question is also way too general. Each individual may be dependent in ways much different from another.
Worst case: The Human Vegetable - a person with no way of caring for themselves and is at the mercy of others for survival. Even with all of the incentives by government not to help, people still do. So there’s nothing to suggest that these folks would be left to die. In fact, there’s evidence to suggest that these people would benefit from a vastly more efficient method of charity.
The Poor - there’s no singular reason for a person to be poor. Capability, ambition, opportunity, judgement, etc. can be factors that determine whether a person is poor or not. The government attempts a one-solution-fits-all approach, and ends up making it largely ineffective if not even worse. My opinion is that the most meaningful way to help the poor is by human associations and instilling dignity. That tends to be a voluntary endeavor. I tend to believe most people will rise from their condition to do things that matter to them and benefit the rest of society. The use of force in that equation just doesn’t work.
The Elderly - this tends to be the group statists target the most with their fear tactics. Health care expenses have increased due to government intervention, so eliminating that can certainly help. A segment of the elderly have bought into the government retirement plan, which is essentially a ponzi scheme. At the same time, the goverment has also put into place conditions that practically force older folks to retire in the first place. That portion of the elderly who have bought into all of the statist promises will have to adjust to reality and may need the charity of others. Again, there is no proof that a free society will allow the elderly to just die in their beds. Government, on the other hand, is prepared to do just that as their solution to health care costs.
The Children - among all of the dependent, this group represents those who have the most to gain from a free society. Whatever setbacks they experience at first will be more than offset by the gains down the road. And again, there’s no proof that a free society will just forget about these people. There’s a lot of cultural issues that go along with children, so whether you have a state or a voluntary society you’ll still see some problems that people might not agree with. Everyone seems to be an expert on how to raise other people’s children.
The Minority - it is the state that concerns itself about majority-minority, gender, race, class, creed, etc. A free, voluntary society concerns itself on individual value. It’s human nature to associate and trade with whomever you want to, but by excluding others you tend to put yourself at a disadvantage. In the US, the state established the majority as the ruling group. The state prohibited women and non-whites from participating in government, from owning property, or even making such people property. The state has had its hand in things from the very beginning, leading to most of divisions people have experienced. Those parts of the country that were outside of state influence or control tended toward a greater degree of cooperation across many different groups, until the state re-inserted itself. The state creates sides and then sets both sides against themselves - all for the purpose of keeping power and influence over people. The state is just a group of people who do not support a free, voluntary society. So you’d think that by getting these folks out of the way, minorities would be much better off. For one, they wouldn’t be minorities any more, they’d simply be human beings.