For rare coins which were frequently mounted, the mount (or removed-mount damage) has a negative impact on the value, but does not immediately clasify the coin as "junk".
The classic example of this has to be the
Boer Republic's "veld pond", struck in South Africa while the Boers were on the run during the second Boer War. The mintage was very small (under a thousand), the artwork wasn't all that great to start with, and it's estimated that about half of them were turned into war trophies by British soldiers or Boer veterans after war's end. Never-mounted coins are probably worth twice as much as mounted coins, but both are worth far more than bullion value.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis