If you read the datasheets on the components they usually list a one time short duration high temperature period. This is intended for soldering it to the board. Basically they do start to fail. The plastic starts melting or evaporating and the wires might start oxidizing. But when it is such a short duration, and only once, it will usually not cause enough damage to the component. Even then you need to test each assembled board after soldering to make sure it still works. Some components fail as it is soldered.
It helps that solder is specifically made from as low temperature metals as possible (while balancing other properties of course). [Wikipedia](https://en.wikipedia.org/wiki/Solder) lists the average temperature of electronics solder at 180°C to 190°C (of solder that might be used in electronics). So while this is certainly hot enough to hurt hands and burn plastic, it is far too low to melt the metals that are used in the electronics.
A lot of times, if you run a piece of paper over a flame, it might turn a different color but it won’t catch fire. It’s only when you hold the paper near the flame for a couple of seconds that it ignites. But the longer you hold the paper near a flame, the more likely it suffers permanent damage instead of just looking a little toasty.
Also think about a popsicle. It doesn’t instantly turn to a puddle even on a very hot day. It takes a while for it to melt.
The electronic components are like that, too. The high heat will damage them *if it persists long enough*. The goal of the person doing the soldering is to try and minimize the amount of time heat is applied. The longer the component is heated, the more likely it suffers damage. If the person has difficulty with a part, they might have to back off and give it time to cool before continuing.
They *can* be burned. But a person who works with skill will move quickly enough it doesn’t happen.
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