Someone who wants to live a nicer life than the one that can be afforded on ~$12,000 a year...aka pretty much everyone. The problem with labor today is not a shortage, but an oversupply. In the short term, people would perhaps have to pay delivery drivers more because some would be tempted to sit on their couches, so the costs of delivery might increase somewhat (keep in mind that corporate profits are at record highs, so depending on the company they might be able to just absorb the wage increase...but let's assume that doesn't happen). The people living off their basic income might be less able to afford to order takeout, and would have to either suffer the inconvenience of cooking their own food, or they would have to get a part-time job, say as a delivery driver, helping to push the costs of delivery back down a bit. In the meantime, the delivery drivers would be reaping the benefits of increased wages due to lower competition, spending those wages in their local economy on things like takeout and keeping the overall economy strong enough to support the taxes for basic income (which they also receive, so they have no reason to complain about or oppose it. Sure they wish their taxes were a little lower, but they got a raise last year, so it's not the end of the world, and they like the security of knowing that if something happened, they wouldn't be completely destitute.)

The only way we would ever actually get to 90% of people not doing productive work is if automation gets to the point where it can meet all the needs and wants of a typical individual with basically no human input. Otherwise, there will always people who want more than what can be afforded on the basic income, and are willing to take paid employment to get it. Wages and prices will find equilibrium based on how much people want stuff vs how much they don't want to do the work required to produce it. With a relatively low basic income, this equilibrium isn't even going to change very much from what it is now. In the situation with 90% unemployment, your takeout is cooked by robots delivered by a drone and the only costs are the energy required to produce it, plus a small profit to the owner of the system. Since everything is automated, it can be deployed at large scale so even tiny profits add up quickly, and assuming we have managed to keep a relatively free market, competition will keep profits down and make sure goods stay affordable. At that point, people aren't going to be getting jobs whether they want them or not, so if we haven't implemented basic income by then, I sure hope we've come up with some other solution for how to get people their needs when there is literally nothing they can do that can't be done faster and cheaper by a robot.