Under welfare? What do you mean? People on Welfare don't receive the money unless they opt out of welfare, and if they do, they get the 1k instead, which isn't nearly enough to give up on welfare entirely.
If people who work get it, the people who need it the most should still get it with no conditions. Should be given to people who are even on welfare, but I understand the decision from a legislative standpoint. Conservatards won't agree to it if welfare recipients get more money, but might be more willing if they can use this 1k to slash welfare funding.