Ultimately, as with everything else publicly funded, it is tax money. You work, you pay tax.
In case of Basic Income, you can decide not to work and "drain the treasury", so to speak.
Though, you wouldn't get as much money as if you decide to work and pay taxes. The Basic Income is lower than the income you get from working.
So you still have incentive to work.
The money used for Basic Income is roughly corresponding to the amount of tax money used on various social benefits (unemployment benefits, disability benefits etc.).
Only that this time, you don't have to work to get those money. In many modern welfare states, you have to work in order to get social benefits, like unemployment benefits. You work as cheap labor for the government, in todays welfare benefits. This is what I want replaced with Unconditional Basic Income.