The idea of basic income is to provide something. Enough money to ride public transport. Enough money to rent a room (location dependent, but even in my neighborhood rooms can be $300-$600/mo). Enough to buy food.
It is a lot easier to look for a job when you aren't spending your entire day trying to stay out of the sun and scrounge up enough money to eat. It's a lot easier to look for a job when you don't have to choose between food and public transport.
It is very difficult to scrounge up enough money to take care of the basics while job searching. It isn't impossible but it is very, very hard.
Basic income helps to prevent people from falling that low. If you were moved by a woman struggling on $10k~, try listening to the struggles of the homeless in your area. If you are fortunate not to have any in your area - go to somewhere you know they are. Just talk to them for an hour, it'll change your perspective a bit.
My biggest issue with BI is the logistics behind it. To get it to work is complicated, seemingly prone to corruption, and possibly not sustainable. But it is going to be necessary to figure it out in the coming decades, IMO.
