I work with our local food bank, and got in a discussion with a family member who was shocked at there being no means testing or proof of need to participate. I'm certain there are people we serve who are over whatever threshold would exist, but the cost of excluding someone who's hungry because they couldn't print a paystub or have access to the right documents is _so_ much higher than any spillage from fraud.
With certain aspects of society, such as with social-saftey-net benefits, when the costs of exclusion impact those teetering on the edge, "non-zero" fraud is absolutely the optimal amount.
1 - https://www.bitsaboutmoney.com/archive/optimal-amount-of-fra...