We have progressive taxes today, and the only people working under the table are predominantly the poorest, who cannot afford taxes and have less to lose. The richer you are, the more you have at risk getting caught for tax evasion, and the less likely you are to do it, until you get so rich and the amount lost in evasion so lucrative you can offset the risk by buying politicians, courts, and police while also writing the laws and having significant fail-safes protecting your money laundering.

But that would happen anyway. If you are taxing the ultra-rich period, at almost any % of income, there are strong incentives when the taxable total is in the millions or billions to evade taxes.

There are already lots of people willing to work under the table at low end positions, to avoid having taxes taken out of their pay. There's plenty of incentive. Seems like the way to curb this is to target employers rather than employees. That's why it's generally harder to find an under the table job than a legal one, because it isn't worth the risk to the employer to pay you off the books.

It still happens, but I doubt a BI would significantly impact this one way or the other. Right now, people in the bottom percentiles of pay get most or all of their taxes refunded, but still like to have under the table jobs to maximize what they take home every payday, and under BI, they would still likely remain unaffected by tax increases. The middle class would likely be affected, but they tend to work jobs that aren't as easy to do for unreported cash, and have more to lose from an audit if they get caught, so its still safer to work legally. The richest would naturally get the highest absolute burden, but they are likely already doing all they can to avoid taxes, since they can have a lot of effort put into it relative to the potential gains, so I don't see a huge migration to illegal undeclared income there, either.