Event hosts will probably know when an emotional speaker has gone from having a cathartic experience to a destructive one. It is entirely appropriate for the host to step forward and try to manage the moment in a healthy and supportive way. Of course, emotional honestly does not excuse any sort of abusive or threatening language; at that point -  as at any public event - the speaker will forfeit their right to continue.
If a listener has an uncontrolled emotional outburst, the host should loudly and firmly remind people that the audience is there to listen, not to engage in debate or critique. An effective method for neutralizing a lone problematic voice is to ask the crowd for a quick show of hands, or a voice vote, on whether "we should continue engaging with this individual or move on and ask that they keep their peace." Invariably the crowd will want to move on. That kind of peer pressure is almost impossible for an individual to counter, and they will usually get up and leave the event.
It's also true here that an ounce of prevention is worth a pound of cure: Make sure that the event guidelines are clearly communicated to all attendees. Expectations for attendees can be included on the event registration page, on a simple program handed out at the event, and in the host's introduction.