Information is not in on how the Muslim immigrant terrorists who struck at the Boston Marathon immigrated to the United States, but it is reported that they are legal permanent residents, e.g. green card holders.
It is also reported that they are Chechen or Kirghizian. Given that, it is highly likely that these terrorists, who apparently are highly motivated America hating Islamists, came here via asylum. Muslim fanatics who are fighting their less fanatic Muslim countrymen and attacking Christian Russians as well, from the Chechnya area are generally admitted on the basis of refugee status or asylum status.
Contrary to popular opinion, there is no significant screening of any immigrant group, including asylees and refugees. There is a fingerprint check and a name check, and that is it. There is no investigation into the beliefs of the applicant for immigration status, even when they come from terrorist source states. It is no surprise then that we admit tens of thousands of Islamist fanatics from Palestine, Somalia, and Chechnya. And consequently no surprise that there is blow back when we admit individuals who no surprisingly turn out to be terrorists.