Incentives to be productive don't go away, can you create something other people want? Art? Literature? Take a loan or find investors. Worst case scenario you end up back on welfare.
Welfare needs to be thought of as a cost, not an investment.
That's a not-entirely-unreasonable (though, still, I'd argue basically flawed) idea for welfare in an economy that is heavily labor dependent and in which the presumption that being jobless is a short-term, transitional situation and where the share of output going to labor (as opposed to capital) is relatively high.
One of the reasons I think ideas like BI have been catching on more recently is that it is increasingly obvious that the economy is, to the extent it ever was like that in outline, increasingly moving away from it and not likely to return to it.
> Incentives to be productive don't go away
With a guaranteed floor rather than guaranteed addition, yes, within a certain range incentives to be productive go away, because any gains up to the amount of the guaranteed floor have zero net return to the person producing them.
Because basic income respects human freedom, and as automation advances and the rewards of the economy in pure-market terms increasingly shift even further from labor to capital, a basic income that is adjusted in amount as the economy shifts provides a comparatively light touch redistribution represent rents on the commons that maintains opportunity (as the recipients can choose how to allocate the basic income between present consumption needs and investment in personal development and/or capital) whereas "basic welfare" creates a permanently dependent, effectively unfree, class with no mobility, opportunity, or effective choices.