It's kind of weird for them to be trying to file for asylum.
By definition you have to be persecuted by a government to be eligible. And their country doesn't have a government anymore . I would imagine all of their claims are going to be denied. contrary to popular opinion, just having a shytty country is not grounds for asylum.
Personally I'm of the opinion that the best move for the Haitians is to go back to Francophone Africa. I think it would be easier for them to integrate into a French speaking place like Ivory Coast or Senegal. Economically speaking and politically speaking , both countries are more stable than their own. And they would probably be more likely to take them in than America or Canada. Lord knows the Latin American countries don't want them.
The main airport in Haiti has been seized by gangs. There is no mechanism to send them back.