That's debatable. But lets assume it for the sake of argument.
> Should immigrants receive the BLS? If yes, you go broke. If no, the immigrants are essentially second-class citizens who have to work for an extremely low wage (because they would have to pay indirectly for the BLS).
I think this claim is overly simplistic; also, I think there are several categories to consider,that I think you've failed to distinguish:
(1) Naturalized citizens should certainly receive whatever universal or guaranteed income is adopted, but immigrants don't become naturalized citizens immediately.
(2) Legal immigrants (the number and characteristics of whom a democratic state can effectively regulate), who are not citizens, probably should be eligible for the support [1] as well, but may be admitted on criteria that include having means of support that make it less likely that immigrant will be a recipient (in a GMI scheme) or net recipient (in a BI scheme).
(3) Non-immigrant, but legally-present workers, visitors, etc. should not generally be eligible for the support. In the case of non-immigrant economic admission categories, adequate support means should be part of the conditions for admission. There may be some exceptions to this (note [1] again may apply to these exceptions) or some categories of non-immigrant admits that are qualified for alternative, status-specific support.
(4) Those illegally present probably should not be eligible for the benefits, but may be eligible for some kind of normalization of status process after which they would become legal immigrants who might be eligible for benefits (to which note [1] would apply again). This normalization process might include up-front payment of a fine for those with means, or commitment to income contingent future payment of the fine with nominal interest, and might even include limitations on benefit eligibility for some period even beyond what regular legal immigrants might face, or commitments to repay any benefits claimed during a certain transitional period on an income-contingent basis. (In general, payment for normalization -- or payment for above-quota legal immigration -- makes sense for individuals who are not personally barred, since limits on levels of such immigration are a cost-of-immigration control measure, and its better for people who want to immigrate to bear the costs then for society to bear the costs of inefficiently trying to keep them out, and then also bearing the costs of them coming in anyway.)
[1] As productivity advances and if the basic support improves to provide more than a very minimal floor, its not entirely unreasonable that non-citizens might recieve less than the full support level, however, possibly based on a sliding scale based on residency; in theoretical terms, in a rent on the commons model, this represents a kind of "vesting" process where the immigrant doesn't become a full "owner" until they are naturalized; in practical terms it provides basic social support but reduces the immediate immigration incentive.
In some sense we are already working towards a global government by claiming human rights to be universal. Out of that endeavour there will (in the far future) emerge a central authority or assembly which effectively enforces human rights and free trade.
In the US, undocumented immigrants have that problem though. Some politicians praised illegal immigration because that's a young, eager workforce with zero rights and benefits.
Also it seems that welfare states can't really save money by excluding immigrants. At the very least the society has to foot the bill for medical emergencies, so declining them prevention and health care may fire backwards. It's hard to "get rid" of the immigrants' children, so you better make sure they get the same education and chances as citizens do (or you end up with a young, poor and extremely discontent minority). If these children aren't put in good schools and fed accordingly, they will also be sicker and less intelligent than their peers.
That's why I think social security is a very profitable business for state and society.
That way, everybody is taxed fairly - proportionally to how much they earn and consume. So, everybody should also be treated fairly - provided all the basic services that the government provides.
The small, rich countries in the north have a lot less problems with controlling immigration, owing to cold or wet borders, low absolute population and low population density. These countries only recently became attractive to immigrants. They may even be able to deport most of the illegal immigrants.
Germany for example can't expulse illegal immigrants on a grant scale. Justified public outrage about "German mass deportations" would even be the least of problems. It's just logistically and politically impossible.
That's why I say that immigration is almost impossible to regulate effectively with the means available to a democratic nation. You'd need some kind of STASI to hunt down hundreds of thousands of immigrants. Nothing would be worth that....
"Universal credit" is an administrative project to coordinate all the existing systems. The disability payments you linked to are subject to increasingly stringent processes which end up declaring terminally ill or permanently severely disabled people "fit to work" and withdrawing the funds they need to survive. This has resulted in some poverty-related deaths and suicides.
Jobseekers' allowance is also subject to heavy scrutiny. I've heard that the best strategy if you have children is to declare yourself self-employed on a zero-hours basis: this stops the jobcentre from hassling you as you no longer count as "unemployed", you just don't have any work. You can then claim "working family tax credits", housing benefit, and child benefit.
Immigration can't be effectively regulated by any means available to a moderately democratic state. Should immigrants receive the BLS? If yes, you go broke. If no, the immigrants are essentially second-class citizens who have to work for an extremely low wage (because they would have to pay indirectly for the BLS).