Would you stay at a job were the boss belived a lie about you but never confirmed the truth?

Anonymous
So someone a co-worker lied about something I did, and inside of the store owner checking the video cameras or confirming the truth, she just said if she hears this again, it's going to be an issue. I gave my boss a shirt text about what happened and said I would like to talk about it in person, but she never replied back.

Would you stay at a job like this? So I kind of feel like if I have issues with this co-worker agin the boss will just believe her instead of talking to me and asking what happened. I have never worked at a job that just takes 1 person for their word
Would you stay at a job were the boss belived a lie about you but never confirmed the truth?
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