The great depression was global. If the US and England was feeling it, then the Caribbean was definitely going through it. Anyone going back was going back to a worst situation unless they had ownership of something and most of the people that came didn't.
Maybe there were a few that did but I've never seen anything indicating there was a mass exodus of west indians from NYC back to the Caribbean during those days. Also by the time of the great depression a lot of west indians were already second-generation or some came as children and all they knew was NYC. those people were not going anywhere. The great depression was tough but it's not like it was some refuge shyt. a lot of people still managed the eke out a living
A matter of fact the origin of the current day west indian day parade started in harlem in the 1930's. There most have been a community to be able to do that.
As for Haitians in Louisiana. I doubt they went back to Haiti given that there were more opportunities in the states. But what make you think they moved to "California or another country"

. it's so random. what other country? If you have solid info on this I'll happily read it. but never heard or seen any reference to early Haitians in California. If anything they went to northern cities.

please do tell where those foreign born blacks were from
But back to my original point. Alot of black people in America walking around thinking they're ADOS are in fact west indian. The west indians that came here during the early 1900's didn't just move back or to some other country. Yes many married and had kids with other west indians but over the years many had with AAs. Take Malcolm X for example: AA father and west indian mother.
I'm not saying this to take anything from AAs or anything like that. just stating facts. If you're AA from around NYC, Boston, South Florida etc there is a good chance that you have some west indian heritage.
Even some AA's from mid atlantic states might be of west indian descent as a lot of slaves were brought there from the carribean:
None of this is to take away from any of our histories. I find all of this really fascinating