Take this with a grain of salt, as this is my understanding of it all and parts could be wrong.
Exactly what happens if any of the protections kick in, I actually don't know.
As far as I know, there are 5 types of protection for batteries:
Over-current
Over-voltage
Under-voltage
Short-circuit
Overheating
Some of these safeties are beneficial during use, and some during charging.
TL;DR:
Buy quality flashlights, batteries and chargers, and don't cheap out on either of the things. Use common sense at all times, be extra careful at first to gain personal experience with your devices and batteries, and then unprotected cells are perfectly safe to use.
I also used to refuse to use unprotected cells. With very cheap lights, the protection inside the battery was the only way to prevent any incidents like over-discharging the cell, effectively ruining it. But in the last couple years, starting to buy custom lights, I have become comfortable with using unprotected, quality batteries. Such as Samsung 40T (21700) and Molicel M35A (18650). Using a Nitecore UMS4 charger, that has plenty of safety features built-in to protect the batteries.
Expensive and / or quality lights have several of these features built-in, and even with unprotected cells, the light itself won't drain the battery any further by simply refusing to turn on if the voltage gets too low. This is both to protect the battery from being drained too much, and also because the light would only give out a couple Lumen, which would be practically too low for most usecases. But many lights will still trickle-drain the cells (called "vampiric" or "parasitic drain"), which can and will drain unprotected cells down below their safe limits. Which is why I prefer unscrewing the tail cap on a light half a turn, to physically disconnect the battery.
Over-current protection can be an issue with protected cells in custom lights, as the LEDs and electronics in such light are made to drain, say, 10 Amps from a battery. Most top-end protected cells that I have seen can deliver up to 8 A in discharge current. Any more, and the over-current protection will kick in, effectively killing the battery to protect itself.
As a sidenote on over-currents, I prefer chargers with a low charge current. High current heats up the battery, and I don't like any charger that charge a battery with over 2 A. 1 A tops, or preferably 0.25 A. Yes, it takes longer to charge a battery - from an hour to most of a day, potentially, but I got time when I charge things, and it is much safer.
Over-voltage protection is useful when charging a battery. If you leave a cell in a charger overnight, the battery can in the worst case explode without any safeties. But while I personally take steps to prevent this, I have forgotten even unprotected cells in a charger. And this is where having a quality charger comes in. Most, if not all, quality chargers have a cut-off point, where the charger itself will reduce its output to just trickle charging when it detects the battery is fully charged.
Under-voltage protection comes in when the battery senses its voltage delivery gets too low, which is between 2.5 - 3.0 V for a typical, protected 18650 cell. If it gets drained further, it can cause permanent damage to the cell or even ruin it. But unprotected cells don't have this feature, and more care by the user must be shown to properly use unprotected cells. Though if you have common sense, and the faintest glimpse of understanding of electronics, I guarantee it will be fine.
Short-circuiting an unprotected battery can lead to spontaneous combustion and explosion shortly after. This is why proper storage and handling of unprotected cells is much more important than when using protected cells. This goes for all batteries, but make sure, at all times, that nothing made of metal can connect both sides of it.
Overheating is closely related to over-current, and can happen either when charging or discharging a battery. Heat kills electronics, and overheating protection is down the connected device to take care of, either the charger or flashlight. Again, quality devices have this protection, both to protect itself and the battery. The batteries themselves, protected or unprotected, typically don't have any sort of heat protection.
Custom flashlights can often get too hot to hold around the head, especially on Turbo (which to me begs the question why the feature even exists), and there seems to be a general consensus among the experts here on the forum never to use the Turbo feature on high-output (and with that, high-drain) flashlights. Both to protect the flashlight itself, and the batteries.
I personally HATE the integrated USB-C charging feature on flashlights and batteries. Am I expected to trust the tiny brain in a battery, when fitted inside a metal tube, instead of an open, much better controlled, dedicated battery charger with much more space for electronic safeties? Hell, no. I am not putting random current into something that is effectively a hand grenade by design and take my chances. I am always removing the battery from the device, and placing it into a dedicated, quality charger, thank you very much.