How can one's career as a reviewer be ended? In this forum, I am reading this great question (What is required of a mathematics referee?) by a user with the name mathprofessor. There is an answer by a user with the name Buffy which starts with:


  Sorry, but if that's all you do, then your reviewing career is likely to be short, ending the first time you approve a paper that is revealed to have an error.


I am wondering now: How exactly can somebody's career as a reviewer end after some paper they reviewed is revealed to have an error?

Sure, the editor who assigned the reviewer may not assign them ever again, but how exactly are other editors (maybe from different journals) notified not to take them as a reviewer ever again? Is there some way the editor who knows is allowed to reveal the reviewer's identity? Or some higher authority they can talk to? Or how does that work out in practice?

Let us assume the following:
If the answer is field-specific, let us assume we are talking about math.
Moreover, as in the other question, let us assume there is no fraud going on -- the author made a honest (but big) error in the paper, and the referee was too sloppy in their report and did not note the error.

Additional question: Are there known cases where reviewers had to end their reviewing career because they did not notice an error? Again, I am assuming no fraud is going on.

Edit: I want to say that the user with name Buffy edited the answer in question and made a much weaker claim. This solves my confusion. Thank you very much, Buffy!
No, the answer is simply that @buffy is wrong.  In reality, editors work hard to find anyone willing to review a paper.  They will be hesitant to exclude anyone.  In most fields reviewers are anonymous, so only one publisher will know if a reviewer does a bad job.