Short of internment camps, how does any welfare/safety net program address this?
People sublease housing units without permission (and even outright illegally, even before considering rental contract limits) all the time. This includes units that are subject to one form or another of public support, whether its rent control or section 8. So, yes, you absolutely can sell (as for Food Stamp benefits, usually at a value less than the subsidy) the benefit you receive from a housing voucher.
After-school programs only work if the kid actually goes to them.