What exactly makes you think that communism is going to remove people having power over other people? That seems to just be intrinsic to humans in general, your economic system isn't going to change that.
And you can absolutely have social support systems in place if the populous pushes for them. Homeless shelters and welfare aren't impossible ideas, they're actively implemented across the world. The same goes for basic needs like healthcare.
Just because your government or community hasn't implemented it doesn't mean it's not possible to do so. It means you need to convince those around you that it's a good idea.