Are you sure that you have pinpointed the original source for the problem?

Is it really the culture where they come from that is the problem?

Isn't it just a problem with the poor and broken-down people in general? It doesn't matter if it is an illegal immigrant or a native who have lived too long without a job and/or a clean bed?

Another thing is that when a native or a foreigner behaves as expected, you don't see him/her.

When a foreigner (or someone looking like a foreigner) behaves in a way you do not like, it is very easy to specifically remember the person as a foreigner.

Selective memory is a common phenomenon, and something you have to be very careful with. More than one person have complained "everyone does ..." and after actually counting found that "everyone" may have been just a few percent.