For example, “flammable” and “inflammable” both describe an object that can easily catch on fire. I can also think of “ceased” and “deceased”, both of which can mean someone or something has been brought to an end.
edit: Some people are including words that can also mean its opposite (like sanction or table), those are cool too! The more weird words, the better!
Valuable member of society
Invaluable member of society
Neither case leads to a tangible valuation of the member as both have positive meanings. Invaluable is sort of like valuable+1, but both are just invaluable superlatives.