Cold pasta salads last a couple of days in the fridge.
Sandwiches can be either in the fridge for next day or frozen & taken out.
It's easy for a kid to take a sandwich out of the freezer & leave to defrost.
Junk food e.g. sausage rolls, pasties, precooked cocktail sausages (most of the stuff in the party food/picnic section) can often be frozen then taken out to defrost in fridge if you are feeling too ill.
Individually wrapped brioche or pain au chocolat usually have a few weeks bb date.
Alpro soya desserts have a shelf life of many months.
Fruit smoothies from supermarket usually have a month plus for brands like Innocent or Naked.
Cheeses like Philadelphia or Dairylea have months on them as do most pates in pots e.g. granovita pates (not recommending meat pates as they are too rich for young children) or potted meats (remember sardine & tomato?) & can go on crackers or crispbreads etc...
Those weird little packets of breadsticks & dips/cheese/ham they sell for kids packed lunches have months on them.
Cheese strings, frubes etc... have a long shelf life.
Pepperami, mini babybell etc.. have months on them.
Pots of fromage frais, jelly etc... usually have at least a few weeks if not months for the jelly.
Carrots, apples etc... store really well & last longer than things like bananas.
Beans, tinned fish etc... can be eaten cold if a child can use a tin opener & things are that bad (which I don't think they would be)
All of these require you to either be able to open a packet or the fridge/freezer so are suitable for children not old enough to use kettle or cooker.
I taught my (slightly older) son to pour water from the bigger kettle into a plastic jug then from the jug into things like cup a soup.
The jug is smaller & easier for him to handle.
My kettle now is a water dispenser type though so doesn't have to be lifted - you just stick a container under the spout & press go.
He still uses the jug as for some things the kettle makes too much hot water (dispenses 300ml)
If you have one don't forget to teach them to fill the kettle after using so it doesn't boil dry.
Not ideal food, but better than going hungry surrounded by the makings of a hundred dinners.
Teaching your child to take things out of the freezer to defrost the evening before means you can bag up bread a few slices at a time for them to get out if needed while knowing how to spread stuff on bread/crackers & how to open packets gives you masses of options.
If they can open tins too, you have things like mandarin segments, ratatouille etc... as well (you might have a powered tin opener which are easier for kids to use)
Don't forget drinks.
Long life fruit juices in lunchbox sizes, things like Yazoo milkshakes have about 3 months shelf life.
In the unlikely event you need this sort of thing, there are plenty of options.