Interesting conflation of issues.  Perhaps a similar conflation of Swift's "A Modest Proposal" would solve both problems.  

As the Homeless Humans have proven adept at collecting empties for a pittance the state government should redirect their foraging skills to their fellow ferals, instituting a US$10 Bounty on felines.  Captured kitties could then be recycled into foodstuffs for those in dire need of sustenance.  

Problems solved.