Immigrants usually have zero desire to go to remote, poor areas. Maybe at some point they did, but today they target large urban areas. That makes sense - if locals can't make use of a piece of land, recent immigrants will struggle even more.

There was some immigration but it was insufficient to revert the trend. Maybe because the immigrants were mostly poor catholics and thus not very desirable partners.

Legal ones who were vetted or just random people off the street?