With current safety nets, we have perhaps 15% [1] of Americans that for whatever reason lack the capital to have an adequate supply of food.
With Basic Income, perhaps we reduce that number down to 1%, but we still need to take care of that 1%.
With the government services program that I suggested (and there are many other models, and I'd be happy to discuss other models), maybe you get that number down to 0.3%. Yet, as a country, we still need to take care of those people.
Personally, when it comes to feeding and housing people, my answer to "At what point do we stop" is: Never.
[1] 48.1 million Americans lived in Food Insecure Households (http://www.feedingamerica.org/hunger-in-america/impact-of-hu... 317.3 million Americans in 2014 (http://www.usnews.com/opinion/blogs/robert-schlesinger/2013/...) = 15.1%