They probably thought that this money was their due. The Infidels should pay the Muslims, as per this verse of the Qur'an: "Fight those who believe not in Allah nor the Last Day, nor hold that forbidden which hath been forbidden by Allah and His Messenger, nor acknowledge the religion of Truth, (even if they are) of the People of the Book, until they pay the Jizya with willing submission, and feel themselves subdued." -- Qur'an 9:29
We recently saw that a jihad-martyrdom suicide bomber lived off Swedish student aid. And as British jihadist Anjem Choudary just said: "The normal situation is to take money from the kuffar. You work, give us the money, Allahu akbar."
"Tsarnaev family received $100G in benefits," by Chris Cassidy in the Boston Herald, April 29 (thanks to Andrew Bostom):
The Tsarnaev family, including the suspected terrorists and their parents, benefited from more than $100,000 in taxpayer-funded assistance — a bonanza ranging from cash and food stamps to Section 8 housing from 2002 to 2012, the Herald has learned.
“The breadth of the benefits the family was receiving was stunning,” said a person with knowledge of documents handed over to a legislative committee today.