The entry for damage reduction does not state that the creature can voluntary lower its own damage reduction, like it says for spell resistance.
Can a creature choose to be harmed by an attack its damage reduction would lower/negate?
An attacker knows when the attack has not worked because of DR, be it instantaneous healing or just invulnerability.
So, inspired by @GeofreyBent's comment, here are several situations:
A Leonal is incognito in Sigil doing undercover shenanigans. Some pesky quasit decides to stab him with a non-silvered weapon, just to expose him.
A werewolf wants to impress some adventurers that he is just a polymorphed mage, and not a werewolf. So he wants to be cut by normal weapons.
A barbarian wants to cause a ruckus (they started it) by "getting stabbed" from some street urchin.
The same leonal from before wants to donate some of his blood to a ritual by a good wizard... How does he even cut himself?
creatures that trigger special qualities "when damaged" like a wolverine's rage.