Yes, you are pretty close to the possible answer, which is still veiled in theoretical rhetoric, but this is to KM as well.
One of the most popular and most discussed models would shutdown pretty much every single existing bureaucratic model for handouts - pensions, child allowances, unemployment checks, early disability pensions, housing allowance,, student allowance... you name it we got it: they'd be gone for good, reallocated into a single source and entity. The amount of money and manhours that would be saved annually simply from getting rid of a few processes in our highly complex and slow system would be tremendous. On top of the already high tax rates, it could be pulled off, not to mention that a bulk of the money automatically returns to the people and is slightly taxed as it would be used to cover necessities, the biggest for most being rent, living compensation, utilities and food.
The other factor here is of course limits to income. People could choose a model that is to their favor. If they already have a high-paying job, say 80,000/year, they could probably be exempt from receiving the basic income, there is no clear need and if they chose not to, they could receive tax cuts or reimbursations on a smaller level. Much like many other allowances in here work, if you make a certain amount of money, you will not be able get the allowance anymore, it would have to be tweaked accordingly and indexed to the average level of necessity costs.
As for the work or cleaning KM mentioned, there will always be people who do not wish to rise higher in society, or got to schools, or those who are not qualified to do more else - the point is that the pay for these "shitty" jobs at the moment is ridiculously low considering our tax rates and cost of living, which is in Helsinki one of the highest in the world. Some people become bus drivers because they need a job, hating it, others become bus drivers because they enjoy what they do. Those people will never disappear completely, and the basic income would be a fail-safe more than nothing else. After all other insitutions of welfare would be shut down, it would be the only option to go on and getting an indexed 700 dollars a month if you are unemployed will not get you far in Helsinki, it'll be just enough to maybe pay your rent and help you not starve to death - it wouldn't be much to celebrate and simply use to enjoy life.
But the benefits of the basic income far outweigh the cons when it comes to an actually working, less bureaucratic social welfare society. Like I said earlier, it would be nearly useless to abuse the system due to small amount of money received, it would help both the people enjoy their lives by giving them and their employers the ability to pay less for one and instead hire more, making it easier for us to choose when and how much we work, because we are not here to simply work anymore, we are here to live. Then again, if someone wants to keep on doing what they've always done, it's up to them - there would be no dramatic change for those who do not feel they need change.