Agree with Togakure & Chuchip regarding cats behaviours.
They are not disloyal...but if you treat them badly, and they find a better deal...don't expect loyalty.
It is very possible that this cat was abandoned, otherwise it is just in at least a semi-neglectful home.
We have a block of apartment buildings out back and every year there is a batch of cats that are left behind by owners who move. Sometimes these cats even have collars. You can watch as their condition deteriorates.
Anyway, first thing to check is if there is a collar & tags. Not having them is no guarantee, though. My cat regularly loses (deliberately?) her collar in our hedges. After losing 3 in a week, we stopped bothering. You could try putting a collar on, with an attached note as someone else suggested, to try and find if it does have an owner. If it is not used to a collar though don't count on it staying on for long.
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