But it isn't. A fifth of the UK working age population, for example, is neither registered as unemployed or earning money. Most of them aren't homeless, or entitled to disability benefits and aren't registered as unemployed because for whatever reason they don't need the money. All of them would be eligible for basic income.
You can afford to provide much better support for homeless people (many of whose bigger problems cannot be addressed simply by providing them with a regular income) if your budget isn't being stretched by the need to subsidise the perceived basic needs of huge numbers of content people that aren't actually interested in claiming subsidies.