I think this might be part of the issue though - I saw another article about this plan that said people often _don't_ try to contribute because their welfare benefits are subject to them not doing certain things.
For instance - you get $X from welfare, you could make $Y doing some work despite your disability, but $Y < $X, and if you make $Y, the government won't give you $X - therefore there is no reason to pursue $Y.
Even if you don't have money, often if you're on disability anything that might show you aren't "so disabled" can stop it. Therefore even if you want to, there is really a strong reason not to try to do things.
That is what basic income is meant to really alleviate - there becomes no reason not to do other stuff, because it's unconditional - those already on welfare no longer have all those requirements.
I'm not saying it would be perfect, but I do think it would address at least part of this problem. I wish I had an actual study on the numbers of people that don't try to get jobs/be productive while on welfare because of the risk of losing the primary income stream they get from welfare, but I can't find anything. I have known several people in this situation though, and watching the system treat them that way was kind of heartbreaking.