What I've seen normally happens is that as a community is displaced, they tend to move to the same areas where other people from their community are living.
For instance in Minneapolis where I live, once they put in a lot of low income housing in, a majority of the whites move out of the city, and into the first ring suburbs. Then several immigrant populations moved into Minneapolis and pushed a lot of the african-american population into that first ring of suburbs where the whites had moved. Sure enough, the whites pushed out into the next ring of suburbs.
This has happened several times and now the ironic thing is they're taking out (or demolishing) all the low income housing and putting in swanky town homes and condos and guess what? All those families (and their kids) that moved out in the 60's and 70's are the prime movers for the new era of gentrification.
My point here is even though communities get shuffled and pushed out due to gentrification, they tend to stick together regardless and create new communities where they move to and find like minded people who have the same common cultural traits as themselves.