Well I work at my kids' school too, doing Lunch Supervision etc.
IF a child forgets their lunch, they can simply buy a school lunch.
This is a public school. Kids' have lunch accounts, into which the parents put money.
IF a family cannot afford school lunch, the public schools have a Federal program, which then allows a family in financial hardship, to have free, school lunches and breakfast. EVERY year, at the beginning of the year, paperwork/forms are sent home to ALL families, about this program. Anyone can enroll, and they need to provide their personal financial info, in order for the Federal program's guidelines, to be met and the family will or will not qualify.
IF a child's school lunch account is empty (because the parent did not put in enough money)... the school, will still feed a child. A note will be sent home to the parents, to inform them that their account is in negative balance, and to send in payment. The parent can then, just send in the cost of just that one lunch, or the amount to cover their child for the entire month etc. It is up to, the parent on how much to put into their child's lunch account.
We never, let a child go hungry. The staff, will provide something.
NOW, per the cafeteria, it is a State Wide rule. Each cafeteria has to keep stats... on how many lunches are made each day etc. And what the needs are etc. IF a child is given a lunch, with no payment made... then how does the school cafeteria cover it. EACH day, the cafeteria makes a certain number of lunches, BASED on, how many kids are eating school lunch that day and how many kids have brought home lunch. EACH morning in class, the Teacher takes a count of how many students brought a home lunch, and this count is immediately sent to the Cafeteria. Cafeterias have to keep count... EACH day, and keep their stats, too. FOR the Districts counts which is then, stats for the State Dept. of Education, and which ALSO impacts, the Federal guidelines on how much money each school gets etc.
So, it is a lot of things... to consider, when only just one child, forgets his or her homelunch.
And per donated "food." These are sometimes regulated too, per the school's District, and there are rules about what kinds of foods can be fed to the child. It is per nutritional guidelines per the State, and/or if a school has a "no nuts" policy etc.
AND it also depends on the budget of a school.
And the storage of these donated foods. Most schools are tight on extra space and storage for example. AND then, who will inventory all that donated food and keep accounts of it???
Many things to consider.