In reference to the classic Indestructible Edible Trope, how long can an adult subsist on largely junk food? I realize that "largely" is vague, so feel free to clarify as desired to give a helpful answer (one way or the other). To motivate things:

Imagine a world shortly after the apocalypse. Something very quickly resulted in the "depopulation" of most of the USA (or similar country). Best bet is a virulent plague with a 95% mortality rate. Because of how quickly it spread and killed people, those who survived the plague have basically found themselves in a "fairly" undisturbed world. For the purposes of this question that mainly means that grocery stores, gas stations, etc, are mostly still stocked with goods.

Of course power goes out quickly, so anything that needs to be refrigerated goes bad very soon. This leaves hardier staples, but from what I can tell the longest lasting foods are largely pure carbs with very little nutrition other than calories. Some examples:

1. Dry pasta (1-2 years)
   


2. White rice (4-5 years, but only 6-8 months for brown rice)
   


3. Unpopped popcorn (indefinitely)
   


4. Cereal (6-8 months)
   

My own impressions lead me to believe that these are also some of the more common items in a grocery store, and so they would be the easiest to find in large quantities for a post-apocalyptic scavenger. However, these foods (especially white rice and white pasta) have very little nutritional value other than calories and some minerals. Certainly very little protein, and no fat - fat especially would make them go bad faster, I suspect, so high-fat foods are most likely out after a few months (although I think canned nuts might last 6 months or a bit more).

Still, our survivors need to figure out how to become independent and produce their own food without the help of modern infrastructure. For the purposes of this question our survivors apparently have access to sufficient quantities of clean water as well as shelter. We're ignoring the risk posed by large quantities of dead bodies rotting everywhere. The survivor(s) are small in numbers and we'll presume there is enough food left in stores: the only thing that will hamper their long-term scavenging is the expiration date of the food (the actual one, not the one printed on the back).

How long do our survivors have to figure out how to become self-sufficient with food sources before malnutrition becomes a serious problem? Or can they survive more or less indefinitely off of such low-quality food? I'm also open to frame challenges, aka let me know if there are actually more than enough nutritious and long-lasting food sources around and there is nothing to worry about.

A few months at best

It's the lack of vitamins that gets you.

Vitamin C deficiency is known colloquially as scurvy and was one of the biggest killers of sailors in the age of exploration.

Simply, you need your fruit and veg or you're going to die.

You can get around this if you have supplies of concentrated fruit juice or vitamin supplement pills, but you've got to have those vitamins.

Even if you have vitamin supplements stored, lack of fats will kill you before lack of protein. There's a phenomenon called "rabbit starvation" -- someone surviving in the wild whose only meat is wild rabbits will die in a few months because there isn't enough fat in the meat -- some vitamins are fat soluble and can't be absorbed, even with adequate vegetation in the diet, without enough fat intake.

Protein catabolism is a genuine issue: it's why people in WWII concentration camp photos look like living skeletons; their bodies have metabolized their own muscle to keep their brains and organs running. But if you have zero fat in a calorie-sufficient diet, you'll still waste and die even if there's enough protein to avoid digesting your own muscles.

Not a problem.

There are literally food sources all around us. The only way your survivors would have to survive on "junk food" is if they were somehow trapped in an industrial city or in the middle of a desert, and even then they would learn to find alternate sources of food as part of surviving. If it's a situation where they have adequate clean water, they'll be able to find edibles.

Once they manage to get into the country, they should very quickly find other survivors who actually know how to grow food and/or have a rough understanding of which wild foods are good to eat. Heck, they'll find good food literally growing on trees or out of the ground, if they come upon an orchard or a cabbage farm.