That makes a number of assumptions.
1. That wealthy people's money can dry up.
2. That wealthy people know this and it provides an impetus to spend.
3. that that impetus to spend is constructive.
4. That poor people, promised basic income, will differ markedly from wealthy people in this respect.
I can't speak to all of these but I can speak to some of them.
1. Certainly wealthy people may lose their wealth. But most don't.
https://blogs.wsj.com/economics/2016/05/19/the-wealthy-in-fl...
https://www.washingtonpost.com/news/wonk/wp/2014/10/18/poor-...
Also see this swedish study which indicates that wealthy kids save less then their parents but still tend to be wealthy, and that this is true for both adopted as well as natural born children, indicating that it's not some sort of genetic advantage
http://www.nber.org/papers/w21409
as for 4, I think you have this idea that poor people are poor because of intrinsic characteristics. This is a more common belief among conservatives (http://www.people-press.org/files/legacy-pdf/1-23-14%20Pover...).
Here's some evidence that it's not an intrinsic quality.
https://www.nytimes.com/2015/05/04/upshot/an-atlas-of-upward...
There's also evidence from things like free meals and early childhood education. Links are probably easy to search for if you google free lunch benefit and HeadStart benefit. Basically giving kids proper nutrition and free preschool make a big difference.
There aren't a lot of studies on giving adults help to get out of poverty though. People like helping kids and young adults, but once you are grown up you are kinda out of luck. I think there is some micro loan data out there though. That said there was canadian basic income, which showed only modest decreases in hours worked, and better health outcomes overall.https://en.wikipedia.org/wiki/Mincome
But even if basic income only effects children of poor people and not the poor people themselves, it seems like it could provide a marked difference in a generation.