Do your verification at the application stage, don't attach income requirements, re-evaluate (gently) with yearly reviews of W-2 income. Don't punish people for successfully getting themselves further towards exiting their troubled situation.

Accept that some people getting help will need it less than others.

There's "fraud" and then there's homeless people trying to get their lives on track. People who need help and support. Saddling them with complex frequent requirements and then calling failing to meet them "fraud" is not helping people.

Be interested in helping people instead of helping only the "right" people.