The general assumption here is that the people receiving basic income do not become lazy good-for-nothing people who refuse to pull themselves up by their bootstraps.
From what I understand, a basic income is supposed to try and soften the harshness of a global economy where there are fewer jobs as more and more jobs are being automated away.
For example, when a factory worker gets laid off, the worker has to apply for unemployment and then wait to receive checks. With basic income the factory worker has been receiving money already so the worker doesn't have to deal with a beurecratic organization like an (un)employment office. The worker will have enough money to survive, and it will be a net preventing the worker from falling into a vicious cycle of homelessnes and so on.
A person that has had a well paying job will not really care for a measly $500 or so a month, and they would probably just spend it on entertainment or some other services anyway, which is good for the economy.
Back of the envelope calculations: The richer person will have an additional $6,000 a year, which(assuming they make $60,000 a year already) is an increase of 10%, which is not that big. A factory worker who makes $20,000 will have the extra $6,000 a year which mill be a 30% increase in what they make. That will definitely easy the burden off of the factory worker, and if the worker loses a job, he still has at least $6,000 a year to survive off of.
I imagine replacing expensive and inefficient food stamp projects with a simpler government -> persons bank account deposit would end up saving a lot of money, too.
EDIT: sorry if anyone got 20 notifications for this. I kept getting a 502 error and after I finally managed a successful post I saw 8 or so posts from me. Sorry!