With a basic income, they can find work for other people (and other people can find work for them).

Basic income is not a necessary condition for that.

But income is.

Meeting the needs of people who cannot pay you is not a job, without some sort of external involvement. Giving them cash is the approach that gives the market the most room to find the best solution. Giving cash to everyone unconditionally gets rid of strange incentives around discontinuities. Hence, a basic income.