Your question shows the problem with a labor market without UBI. Think about supply and demand and apply it to jobs. A job with high demand should have a bunch of people competing for them, right? And a job with low demand should have few people competing for them for the same reason, right? So low demand jobs should pay well and high demand jobs should pay less. But that's not the way it works is it?

How it works in a system without UBI is that the shittiest jobs pay the least because people require money to live and are competing with each other in a race to the bottom to do that work for as little as possible. As an added effect, human labor is artificially cheaper than machines labor due to the requirement for humans to do work in order to live. So technology that should be invested in, isn't invested in, which means productivity is lower than it would be if the cost of human labor weren't so low.

So to answer your question, once everyone has basic income, the people that do the jobs that need doing that people don't want to do, will need to pay more for people to do them, or also allow people to do them in smaller increments. Think about it. Would you do a shitty job for $8/hr? Would you for $20/hr? Would you do a shitty job for 50 hours per week? Would you do it 5 hours per week? These variables are important, right?

Additionally, if people aren't willing to do a job for less than the cost of a machine to do that job, then suddenly investing in automation makes sense for that employer. Imagine a machine that can do a job for $15 per hour. As long as people will do it for less than $15, that job won't be automated. As soon as people demand more than $15, that job will be automated.

Personally, I think if a machine can do a job humans don't want to do, machines should do that job and no human should be forced to do that job with the stick of poverty. Let free people with the power to say no in the labor market, do jobs without being coerced into doing them, and in doing so earn incomes on top of the basic incomes providing them the bargaining power to refuse low wages.

One other thing. UBI also allows people to say yes to working for low wages, or even for free, doing work they really really want to do. Think startups. Twenty people could get together and work for free for however long it takes to get the startup profitable. Right now, that's not possible without VC funding, or without a group of people who aren't worried about monthly survival. With basic income, no one is worried about monthly survival, so everyone can choose to work for free on what they feel is most valuable to work on.

As for immigration, UBI is for citizens and citizenship can be a real bitch to obtain. It also requires legal documentation, which means UBI could even incentivize legal vs illegal immigration. Additionally, if funded by a VAT, immigrants would be paying into the UBI pool that only citizens receive UBI from. This could potentially flip people from being anti-immigration to pro-immigration, since more immigrants who aren't citizens could potentially mean higher UBI for citizens.

If you have another question, please read my FAQ.