Living in a country that happens to be very poor and suffers from things like earthquakes and hurricanes is regrettable, and we should assist Haiti and its people as we can.
But that is not grounds for asylum. Haitians who wish to emigrate to the US and other countries should do so through the conventional channels.
"Happens to" is doing a lot of heavy lifting in this post. The reasons why Haiti is so much more indigent even than other Antillean countries can be directly traced back to policy decisions made by Western powers, from France's decision to force Haiti to compensate its former slavemasters out of its sovereign debt to the US's rinse-and-repeat installation and deposition of Aristide in the 90s. Haiti should be thought of as one of those countries to which the Western powers have special responsibilities because of our past stupid and/or immoral policy decisions towards it, not just somewhere that "happens to" produce a lot of economic migrants.
