This isn’t cash money they’re getting. It’s assistant for, as the graph notes, housing, food, child health care and childcare. The person making $69,000 can spend his money on whatever he wants. The person making $29,000 only has $29,000 to spend as they see fit. The rest is spent only on things that the welfare can be spent on, like food stamps and housing.
The real problem shown in this graph are the cliffs. Namely that is in the earner’s interest to remain at $29,000 of income than to move on to $30,000. In fact, the person earning $29,000 would have to get a raise up to $69,000 to see the same effect. Welfare recipients shouldn’t have cliffs like that.