If the welfare programs are functioning correctly, any decrease in overall population wealth and/or income would naturally have to raise the welfare spend. The alternative would be for the newly poor to suffer and/or die in poverty, because only the existing poor were being assisted by the programs. Incidentally that does seem to be how much of the US safety net is designed to work and we've been actively trying to push more needy people out of the benefits programs, so that's something.

This is a feedback loop. If "spend is going up" is somehow justification for cutting welfare programs or for not funding them, how does that fix anything? The ideal would be to have more than enough funding for all your programs, then work on ideal ways to utilize the extra funding. In the end if there's a surplus you can always cut taxes on the rich again, since US lawmakers are constantly trying to do it anyway.

Yes, the increasing wealth gap has been killing America. That's what this program is trying to address.

Have people been getting poorer to qualify for welfare?

Taking money from the top of the wealth gap and putting at the bottom seems like it should reduce the gap by simple mathematics.