schäbig
shabby
In poor, worn-out condition, often because of age or lack of care. Usually refers to objects, clothing, or places.
Er trug einen alten, schäbigen Mantel.
He was wearing an old, shabby coat.

shabby / mean
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shabby
In poor, worn-out condition, often because of age or lack of care. Usually refers to objects, clothing, or places.
Er trug einen alten, schäbigen Mantel.
He was wearing an old, shabby coat.

The meaning of 'schäbig' depends on the context. If it refers to objects or places, it means 'worn-out' or 'run-down'. If it refers to people's behavior, it means 'mean' or 'unfair'.
Das Hotelzimmer war klein und schäbig.
The hotel room was small and shabby.
In the meaning 'worn-out', 'schäbig' is often used to describe the poor condition of clothing, buildings, or furniture.
Er wohnte in einer schäbigen Gegend am Stadtrand.
He lived in a shabby area on the outskirts of town.
When it is about character or actions, 'schäbig' describes morally low or unfair behavior. Typical combinations are 'eine schäbige Ausrede' (a shabby excuse) or 'jemanden schäbig behandeln' (to treat someone badly/meanly).
Das war eine schäbige Lüge, um sich selbst zu schützen.
That was a mean lie to protect himself.
To criticize someone's unfair behavior, the construction 'Es ist schäbig von [person in the dative], ... zu ...' (It is mean of [person] to ...) is often used.
Es war schäbig von ihr, dir nicht die Wahrheit zu sagen.
It was mean of her not to tell you the truth.
fair
'fair' and 'schäbig' are opposites here when it comes to behavior toward other people. 'fair' means that someone acts justly and decently and does not deliberately disadvantage anyone. 'schäbig' describes mean or dishonorable behavior. It sounds clearly negative. Important: 'schäbig' can also describe old or worn-out things, but in this comparison it is about the moral meaning.

Nach dem Streit erzählte er private Dinge weiter, und das war wirklich schäbig.
After the argument, he shared private information, and that was really mean.
Es ist fair, wenn jeder im Team die gleiche Chance bekommt.
It is fair when everyone on the team gets the same chance.