Here are my two examples so far, from my 4th game / 2nd serious game / 1st serious Ironman Game. Normal difficulty, got to June so far.
Scenario 1 is when... you get jumped and swarmed by Chrysallids - it can be 2 or 4 or 6 or 8 or whatever the number is at that point in the game that turns your Carapace armour into Crapawash armour. In this situation, that number is "1". Everyone falls back as fast as they can. "Fall back by squads; short, controlled PANIC!!!" Everyone's been falling back and firing or just running like hell. You're the least falling-backest. This Chrysallid has already been up in your face twice so you are definitely running, not firing - that's the other guys' job. Unfortunately they have not done a very good job of killing this particular Chrysallid and it is right up in your face again, so close you can see the drops of slime dripping down its jaw/fang/mandible/sticker thing. Your primary weapon is empty, your buddies are all either empty or fired out or hiding behind a large solid object a long way away. And your back is, literally, against a wall. Well moving in a direct line away from the Chrysallid seemed like a really good idea when all the other guys were helpfully firing at it. They hit it, sure, they hit it quite a lot, but it kept on coming and now it's so close you can smell what it had for breakfast. You're pretty sure it had XCom Agent for breakfast.
So what do you do? You pull your trusty little Mk1 Pistol and take aim and pray to all the gods in heaven and for good measure all the gods under the sea or hiding in pyramids on Mars. You pull the trigger and... pop!, Chrysallid nerve centre explodes in a gooey stinking mess all around you. Well you're certainly standing in a gooey stinking mess. Oh hang on, the stinky mess is leaking from the leg seams of your body armour...
Scenario 2 is similar except this time the crap-inducing number was 6 or maybe 8, it was hard to tell, there were so many of them and such close range in dense terrain. Your falling back and firing, everyone is falling back and firing, except maybe you are doing more than your share of firing and not falling back because hey you've got the Heavy Laser and hey you're the Captain, right? Lead from the front, first in last out, that kind of thing right. Except again you have run out of distance to run away and run out of buddies to lend their firepower. Everyone is fired or out, and that includes you. You're backed up into a corner and your Heavy Laser has fired its last burst, and there is a perfectly pristine unharmed Chrysallid right up in your face. Judging by the tattoo of a mermaid on its inner mandible, three or four minutes ago this Chrysallid was Lt Becker. Well, as they say, three or four minutes is a long time in a firefight.
There's no point even drawing your pistol, even it you had one of those laser pistols, with an unscratched Chrysallid breathing acid breath in your face. So you reload the Heavy Laser and hope your boys will take the Chrysallid down.
They don't. They all miss. Every single one of them misses.
The Chrysallid screams and arches back and springs forward, punching its killing mandibles into you. You scream as it tears right through you and you... don't die. You don't die. The stupid insect bastard doesn't manage to kill you. You thumb the activator on the Heavy Laser and it screams its mighty jet-engine whine, and vapourises the stupid insect bastard right where it stands: maximum critical damage.
The boys evac you out on the Skyranger for 18 days of medical rest. You insist on keeping the Heavy Laser with you on the stretcher. You have a suspicion Dr Vahlen might want to try to extract, for her scientific curiosity, the five foot long insect claw that's going in through one side of your thigh and poking out through the other side. As long as you've got your trusty Heavy Laser with you, that ain't never gonna happen.