A very excellent question and totally reasonable thing not to know (congrats on being one of today's lucky 10,000!)

I'm speaking from the perspective of US coins because that's what I specialize in but this generally applies to coins all over the world as well:

Prior to (and including) 1964, US 10c, 25c, 50c, (and when they were made, $1) coins were made of 90% silver. We made A LOT of these, so in terms of outright rarity, most are not rare. Today they're referred to as "junk silver" because in terms of collectibility, they're junk, but the 90% silver content means there's some inherent precious metal value (as of this moment on Jan 30, 2026, they have ~approximately~ 60x their face value in silver content, eg $6, $15, $30, and $60 in silver respectively.)

So that's their basal value that fluctuates with the silver market. But the next layer is actual rarity / collectibility -- if a given coin is desirable enough that it surpasses its metal content, you get a different set of values.

Now to your actual question: Do they get smelted/melted down? The answer is...sometimes. They trade somewhat like financial instruments, based on the assumption that you could melt them down (and there's a cost to doing so), so that's how people value the various silver coins. In reality, there's usually enough demand from people who want to hold physical silver in various forms that they don't actually need to be melted down.

There's obviously a lot more to it, but that's the 5c version ;)

Collectible coins usually get melted as a last resort, if they stay on the shelf forever. The value of the metal is still in the coin though. Think about it: you could buy a very common coin with the same metal, or a slightly rare one. Which costs more? Now take the rare one and put a huge dent in it. Is it worth less than the metal content then?