This would first require ending of right to free movement (otherwise whole Eastern Europe would move to countries with ubs) and then really dealing with immigration to prevent whole Africa from moving to Europe. In other words: no way.
For at least to reasons:
Right now, lots of people move within the eurozone (taking advantage of the freedom to move inside the EU privilege) *because* they expect better income somewhere else. If all get the same default CBI (Conditionless Basic Income), then there is no reason for a spanish guy to move to cold Germany, where he has no social connections just to get a Job. Meanwhile, a German citizen who receives a default european CBI whereever he goes has no reason to stay in rural Germany and do the silly unemployment-support form-filling and burocracy dance every quarter (costing German taxpayers billons for the paperwork alone) if he can't get a job there - he can just more somewhere else where its warmer and he has a better chance of trying his luck.
The fundamental problem with the Eurozone is not that we've got to much of it, the problem is that it is implemented wrong. You know, like managers designing software (*shudder*). We've got a forced currency union without the correct unified fiscal mechanisms and social reforms to match. That's a recipe for failure (Portugal, Italy, Spain, Greece ... anyone?). That's why the Greece problem was/is such a mess. Arm-thick extra contracts that no one reads let alone follows and a eurozone straining at the seams. This will need to be fixed ASAP, one way or the other. Or else Eurozone with burst appart.
Fixing this involves a unified social policy and the easyest way doing that is flattening all wealth transfer into a single CBI across the Eurozone. That's exactly what Saxo Bank expects to happen. ... It would be the best solution and solve quite a few problems in one move, including the tough ones like the Greek people hurting badly after nearly 4 decades of socialist miss-management and defacto national bankruptcy. ... But if you ask me right now I think they're being really optimistic. I'm cautiously hopeful that Eurozone does the turn-around and am totally with the Saxobank analysts on this one, but I'm not holding my breath just yet. Politicians can be quite stupid and right now nationalists and far-right are popping up all over the place left, right and center. I hope it's just a fad, but who knows. The dimwits might just take over again.
As for asylum seekers and imigrants:
What does that have to do with CBI??? They don't get that. It would only be for EU citizens. The fugitive crisis has just about zilch to do with the CBI issue.