Can Employer Cut Pay Due To Walking Out On Shift? Can They Make Servers Pay For Walkouts?

This is in Kentucky. My employer has a policy where if you walk out of your shift, your Pay gets dropped down to min wage ($7.25 for most, $2.13 for servers) for the paycheck. Is that legal? It is in their handbook but I know some places have things in their policies that wouldn't actually hold up.
My other question is whether they can actually make servers pay for walk outs or mistakes. I'm pretty sure this us illegal due to it being a tipped position but several servers here have had to. I'd like specific information to be able to bring up if I ever find myself in this position.
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