A guide for the compassionate and squeamish.
So you’re walking down the street and see a pitiful butterfly, wings broken, unable to fly. Perhaps it is a large charismatic species, like a monarch or a pipevine swallowtail. Perhaps you find a beetle or spider, partially crushed by a passerby. What do you do?
A lot of kind and compassionate souls would pick the creature up with the hope that they can save it. In some cases, they would be right. It is entirely possible to fix the wings of butterflies with simple household materials, and given the fairly long lifespan of larger butterflies (6 months or more) fixing a broken wing is probably worth it. This method probably works on other winged insects as well, and can completely restore the mobility of an insect who otherwise would be facing certain death.
When it comes to bodily injuries, however, insects and other invertebrates have a much harder time recovering. Most insects can lose a limb or two without issue, but any serious mobility issues are a death sentence due to predation and breaches to the chitinous exoskeleton are difficult to heal.
Insects do have an immune system, though not terribly similar to ours, and they can repair minor wounds and recover. Some insects can even regenerate new limbs, especially the bug in question is young and still has many molts to go through before adulthood. The takeaway is that invertebrates seem to be able to overcome minor injuries and regenerate damaged or missing parts, provided the damage is not too extensive.
So if you come across an insect with a minor scrape or a missing limb, leave it be. It will likely sort itself out. When it comes to creepy-crawlies that have sustained serious bodily injuries, however, I believe the best solution is to euthanize it.
The reasons why it might be dying are many (pesticides, old age, disease, internal wounds, etc), but if it looks to be in rough shape it probably is not going to make it, as insect lifespans are short and their healing abilities limited. It’s hard to say if insects really suffer with any certainty, but since insects seem to have nociceptors (pointing to the ability to feel pain) euthanasia seems the most ethical choice when the alternative is possible suffering followed by death.
In my opinion, instantaneous destruction is probably the quickest and most humane method to kill an insect. A boot or a rock works great, though it might seem a bit brutal. It will destroy the entire nervous system of the insect, hopefully completely eliminating the possibility of suffering.
If you don’t have the stomach for it, though, options are limited. Unfortunately freezing is the most accessible euthanasia method for non-scientists. It’s heavily debated as to how much suffering freezing causes, but in this case probably would still be quicker than a slow death by disease/pesticides/injury. When insects become cold, their metabolism and activity levels slow dramatically. This applies to the activity in their nervous system as well — cold insects do not react as quickly as warm ones and do not react to stimuli. It’s reasonable to assume that, for much of the freezing process, the insect will not be terribly aware of what is happening.
I’m sorry I don’t have a nicer solution, it can be really rough to watch something suffer and not be able to do anything about it. Best of luck to you no matter what you choose to do and remember: you are doing something kind.