Can a company demote a person via conference call in front of other people?

Question

Via conference call I was demoted in front of other people for unfounded reasons. This was very degrading and embarressing. My replacement who was also on the conference call, said that the Field Manager had told her that he would be there in person . However it was done via conference call, with my replacement there with me, and another manager, that knew ahead of time.

Answer 1

Yes they can.

Answer 2

It's probably not proscribed by company rules, but it sure is a bad practice.  You have my sympathy.

Answer 3

Yes.  If you don't like it you're free to resign.