Quite simple, you'd borrow a lump sum and the bank would accept on the basis you have a guaranteed income and therefore able to make the repayments.
Therefore, the loan would have to be dismissable in bankruptcy. So a UBI loan basically reduces down to nothing more than an unsecured "personal loan", which is something you can get today, albeit at very high interest rates:
https://www.nerdwallet.com/personal-loans?annualIncomeFilter...