I'm sitting in the "sterile" waiting hall at Chop as we speak - there are immigration booths for those embarking/disembarking here, in addition to checks onboard trains (for others).
Upon reaching Chop, I got off straight away and was ushered into the waiting hall. There, I presented my ID and train ticket to a female border officer, explaining I'm going to Hungary on a train leaving in 2 hours. I was asked to sit down, and after 30 minutes a male officer came with the documents as well as an entry refusal letter for me to sign. I was told (in surzhyk) that I could just relax here and board the train as soon as it arrives, and show the refusal letter in lieu of a ticket Chop-Záhony (though I bought hryvnias in Cierna nad Tisou expecting to have to buy a ticket in Chop, apparently I'm not expected to).
So in summary, though you're obviously not supposed to do this, in practice it's not a big deal to them. Not sure how much it has to do with me being a "low-risk" national and/or the fact that there's not a soul here apart from the officers (and there was only one person other than me on the train from Slovakia)