I don't think it works like that. Last I understood, right to food & shelter is primarily a negative right, meaning nobody can deprive you of those things. Similar to right to movement- nobody is obligated to buy you a bus ticket, but outside of special circumstances nobody is allowed to stop you from buying that bus ticket.
Article 25 of the Universal Declaration of Human Rights recognises the right to housing as part of the right to an adequate standard of living. It states that:
Everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control.
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Doesn't sound like the right to an adequate standard of living (which would include food and shelter) is a negative right to me.
Well, that's how it is according to the UN. I'm attempting to find something more specifically about the USA- the UN's opinions are often pie-in-the-sky...
Obviously reality is more nuanced; notice the unrest of SF residents recently. Many can't afford their SF flats anymore; is that a violation of human rights? Do we need to subsidize their housing?
Clearly there is a positive aspect- Section 8 housing, anyone?- but it seems like that plays a small part in the overall "right".