Un-(adjective) but In-(noun) -- does it ever go the other way?
The only case I can come up with is ingrate/ungratefulness. According to wiktionary, ingrate can be used as an adjective, they quote no lesser source than Shakespeare:
But I will lift the down-trod Mortimer / As high in the air as this unthankful king, / As this ingrate and canker'd Bolingbroke. — William Shakespeare, King Henry IV, Part 1
So, even though ingrate is more often used as a noun, it can be an adjective and if coupled with ungratefulness breaks your rule.