Word for Food that's Gone 'Bad', but is Still Edible?
Which side of the line a definition sits can be the subject of some debate, it is cultural in north American English to separate the terms "good" and "bad" when referring to food, there is no overlap or middle ground.
Both culture and prosperity can play a role in definitions of something so important, it's both important to eat but in north American it's important that the quality be of a particular level, IE: not "bad", by a long stretch.
: detrimental to physical, mental, or moral well-being : unhealthy, unwholesome food
- "Health inspectors shut down several food stands that were using tainted and unwholesome meat."
- "A diet of fried foods and pizza is unwholesome."
You can bend the definition of one word either way, but there's no overlap, it doesn't mean the same thing. The ability to stretch one word to cover both extremes doesn't equate the meaning.
If food has gone bad it's not edible:
: fit to be eaten : eatable
: something that is suitable or safe to eat : something edible
Food that is "bad" is by definition "no good" to eat, unless you wish to eat bad food.
Proverb: "Food you will not eat you do not boil.".
A lot also depends on culture and definition. One Roman proverb is "More die by food than famine.", another is: "Jejunus raro stomachus vulgaria temnit: a hungry stomach rarely despises common fare (also translated: the stomach that is rarely hungry despises common fare) (Horace)".
A couple of Filipino proverbs are: "There is no bad food in a famine." and "There is no bitter crust to a hungry person." A Catalonia proverb is: "In times of famine no bread is stale.". None of those proverbs make the food more or less edible, it is the state of hunger, the need, that makes one more tolerant of a lower standard.
Take for example hákarl (a national dish of Iceland) and hongeo-hoe (Korean); which are cartilaginous fish that excrete uric acid through the skin, rather than by urinating as other animals do. These fish are simply buried and left to ferment, utilizing the ammonia as a preservative.
In the case of hákarl the meat of the Greenland shark is poisonous when fresh, due to a high content of urea and trimethylamine oxide, but may be consumed after being processed.
In the case of surströmming, (Swedish for "sour herring"), just enough salt is used to prevent the raw herring from rotting. A fermentation process of at least six months gives the fish a characteristic strong smell and somewhat acidic taste. According to a Japanese study, a newly opened can of surströmming has one of the most putrid food smells in the world, stronger than similarly fermented fish dishes such as the Korean hongeo-hoe or Japanese kusaya.
Ambergris is formed from a secretion of the bile duct in the intestines of the sperm whale. Once expelled by it often floats for years before making landfall. After months to years of photodegradation and oxidation in the ocean the excrement gradually hardens, developing a dark grey or black colour, a crusty and waxy texture. It has a peculiar odour that is at once sweet, earthy, marine, and animalic.
Those are foods which by some definitions sit on the line, but they are not "bad" per se, they are edible; despite being stored in urine or composed of feces and left to rot.
The closest north America gets to food that appears bad is with cheese or sausage which might be covered in mold, but this is not rotten, it's a harmless bacteria that prevents the formation of more dangerous bacteria. Since it either passes food inspection or it does not it is either good or bad; not both.
The examples you offered, "honey that has crystalized" and "ice cream that has ice all over it" can be eaten as-is. There is nothing that you are required to do to it. Crystallized honey simply has a different texture and icy ice cream is simply ice cream with ice.
Joke: The exception is given by the "5 second rule". Such food is "bad" to eat, but not spoiled or moldy (unless you drop it on mold). There often is no difference in the appearance and even testing might show one such dropped sample is no worse than a sample that was not dropped.
The two concepts "gone bad" and edible are in opposition to each other, like long and short. Even a freeganist makes an effort to avoid "bad food", despite eating out of a dumpster. If it's good to eat it's not bad, if it's bad it's no good to eat.