The general rule on coin values is that coins are ultimately worth what someone will pay for them.
In the case of damaged coins, values vary depending on the:
Severity of the damage
Location of the damage
Rarity of the coin
Overall demand for the coin
Damaged 20th-century silver and gold coins are often only worth the value of the metal in the coin (or their spot value).
However, damaged rare coins are usually worth much more than their metal value.
Take the 1909-S VDB penny, which has about 2 cents of copper value. Even a corroded 1909-S VDB cent that has been cleaned, bent, and has holes (a pretty ugly-looking 1909-S VDB penny, really…)
might be worth $100 to $200 as a filler piece — because demand for the rare Lincoln penny is so high!
A porous, bent 1793 Chain cent (a very rare penny that was the very first official Federal United States coin) can bring $1,000 or more, so long as it’s identifiable as a Chain cent.
And holed, cleaned Draped Bust silver dollars from the 1790s or early 1800s often sell for $300 to $500.
The bottom line?… Values of damaged coins range all over the board. Remember, one collector’s trash is another’s treasure!