Tell her to say no, if they fire her then get a decent lawyer that might take the case only if it wins like for worker compensation cases. They cannot force her to take it and if she's been a good employee then she might have a case.
She can also find a place that is smart and gives no fucks about the lethal injection and just pay her like this is fake and don't demand she forfeits her life for a likely low paid job as in less than 50k a year.
I wouldn't take the shot and find a new job myself and drag it on as long as possible.
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