Sorry, somehow last night's post didn't go up.
I haven't revisited my goal of putting up ideas for the really desperate in a few weeks, and some of this will probably overlap things I've already suggested.
The cheapest foods, generally are those that require a lot of cooking: rice, pasta, beans, and dried peas. The cheapest complete protein foods usually do too: eggs and hot dogs.
White bread is generally the cheapest starchy food that requires no cooking. If you buy the cheapest white bread possible (day old possibly), you can get it for less than $.03 a slice. You can often get 100% whole wheat bread (much more nutritious) for less than $.10 a slice, and with it, you get some incomplete protein. Peanut butter can be quite cheap, maybe $.05 a serving, though it's also an incomplete protein, but eat it with bread, and I believe you then have a complete protein. The cheapest no-cook complete protein is usually milk. Sliced cheese is usually not too far behind.
The cheapest vegetables that don't need cooking can vary a lot, but carrots are usually one of the cheapest, followed by spinach, cucumbers, and broccoli. Tomatoes can be cheap at some times of the year. Iceberg lettuce is cheap, but nutritionally not nearly as good as the leaf lettuces, I'm told. Apples and oranges are relatively cheap year round. Generally, check to see what's in season. Also, check fruit and vegetable juices for bargains.
You can manage a lot of sandwiches and salads with just those ingredients without having to cook. For the sake of nutrition, you really need to include some fruits and vegetables even if you're going for a desperation diet. Check for bargains on older or bruised produce, but include at least an apple or orange every day if you can, even if you're surviving on less than $1 a day for food with no way to cook.