statistically speaking it is very unlikely they become criminals however if it does happen, its usually those immigrants' kids that get involved in criminality or terrorism. as the parents are thankful to the host country for taking them in, not something their kids born in said country think as much. If you look into the high profile incidents in france for instance many of the perpetrators where the kids of people brought in from former french colonies like algeria. a few others came in through greece during the migrant crisis of the past 8 years