I got some admissions offers from Ph.D. programs in the United States. In the near past, I worked as a research assistant for a professor. The advisor was completely unethical and abusive. All his past students without exception say bad things about him: he writes negative letters of recommendation to his students even after agreeing to write strong letters and in some cases, he did send negative letters un-invited to schools that accepted some of his M.Sc. students. I am very happy now that I left him. I mentioned in my CV that I worked as a Research Assistant but I did not back it up with reference letters of course. In case this professor finds out that I received offers and tried to contact these schools, is there a possibility that they might decide to rescind their offers?
All his past students without exception say bad things about him: he writes negative letters of recommendation to his students even after agreeing to write strong letters and in some cases, he did send negative letters un-invited to schools that accepted some of his M.Sc. students.
Short of a serious, substantiated allegation of research misconduct, we would take a letter like this to be weird and immediately disregard it (with a few choice comments about the professor involved --- in a small field I suspect we might already know that this professor has some issues).
If an offer had already been sent out, it wouldn't be rescindable based on this. I'd wager to say that this is probably the same case across all public North American institutions.
First, it is entirely improper for anyone to do this other than cases of student serious misconduct. In this case it is something that he should not be doing. You say he has a history of this, so it could happen, but it would take an extreme personality to do this. Professor Voldemort. Such people tend to be generally disliked in academia. But they can also be difficult to dislodge. But they may also be widely known for bad behavior.
Second, I doubt that any reputable place (US or elsewhere) would simply rescind an offer without recourse or discussion. I assume that you have positive letters of recommendation that you have sent. I hope the letter writers would back up your assessment of Dr. Voldemort.
But, since this seems to be a rather extreme case, I wonder if you can contact one or two of the students that he tried to sabotage with un-requested letters and see what the outcome was. It might reassure you.
And, in case you get asked about an unsolicited letter, make sure that you can respond appropriately. The best way is to have other people advocate for your case.
To avoid being stalked, keep strictly silent to anyone who does not need to know (including friends and best friends) about where you apply to.
Keep your nerve, and be pleasant and professional in interviews, and your target school committees will have the choice whether to believe a well-mannered, and capable student or an unsolicited disreference (which would be very bad manners to send, short of major academic misconduct).
This is not a guarantee they will not be influenced, so try to make all other aspects impeccable, know what you talk about, be well-prepared.
Finally: If they should happen to rescind an offer (which I very much doubt, as it would put them in legal harm's way, but just in case), you could consider insisting on a transparent explanation in firm, but polite language. If they do not offer it, you could, as an escalation, you could raise a Freedom of Information (or analogous) request to get full access to your file (apart from the solicited references whose inspection rights you may have waived) and check what happened. As a further step, you could consider (but IANAL) to mention to them that you are aware about libellous statements about you being in circulation; not accusing them, but putting them into the position to reconsider the situation and that you are aware of that. However, before doing so, you should consult with a lawyer.