My supervisor has a habit of threatening our jobs. I work in a professional corporate office of one of the largest companies on the planet. There is a system of write-ups wherein we would have a conversation about what I did wrong, sign the paperwork acknowledging that we've had the conversation and I've officially been warned with this document that's forever on-record. But lately she has been having just verbal conversations where she'll say things like “I don't wanna have to fire you for time theft” after I clocked out 1 minute late.
For some background, it is a large campus with dozens of buildings in the area. I work on the front desk reception team for a specific building. Some people “float” meaning they work in a different building every day depending on building needs (people calling out for instance).
My coworker got a talking to for something small and silly and she told him “if you can't handle this building I'll put you back in the floater pool” and there is no documentation that this actually happened. As far as his employee records there are no write-ups or anything showing he has ever been reprimanded for anything. And to me it just feels incredibly hostile and unprofessional. If I've done something wrong, let's have a professional conversation and set the expectations going forward and put it in my file. These secret threats are shady AF and I'm not sure I'd have a leg to stand on if I went to HR. What do you think?