Tarnished (Verb)

Tarnished means to make or become dull or discolored

Merriam-Webster’s Dictionary

“A Rose For Emily” by William Faulkner

“They rose when she entered – a small, fat women in black, with a thin gold chain descending to her belt, leaning on an ebony cane with a tarnished gold head.

I now understand this word and the reason as to why it was place in this sentence. The author was describing how discolored and dull the gold head piece actually looked.