The best serious proposals I've seen tend to treat UBI as a form of "negative income tax". Say everyone gets $10k or $20k or whatever, enough to _live_, and then for every two dollars they earn they drop a dollar of "UBI".
If you get $10k guaranteed, then somebody earning $20k exactly thus has an effective income tax rate of 0%, neither recieving nor paying income tax to the government. Anything earned over that starts to be taxed as standard currently.
You'd need to fiddle with the specific numbers, the rates, et cetera, but most serious suggestions are not as trivial as "let's give everyone ten thousand dollars". The principle behind UBI is not that everyone should recieve the same chunk of money from the government, but to provide an income floor that cannot be gone under that should be sufficient to keep people healthy and able to manage. It's a "Universal Basic Income" in the sense that the basic income is universally set, and nobody can go beneath it - you absolutely can go _above_ it.
Relating it to the welfare state is a good comparison, I think. In the same way that socialised healthcare ensures that everyone's bare minimum healthcare is at least up to a good standard, UBI could ensure that everyone's bare minimum income is livable. That doesn't mean that somebody earning $150k/yr still needs that 10k of government assistance, because they are not in need of that income protection (at that moment - of course it immediately returns should they _stop_ earning that much).