Senators debating a bipartisan immigration bill agreed to changes Monday that would bar immigrants who received asylum from returning to their home country, a proposal drafted in the wake of the Boston Marathon bombings.

Sen. Lindsey O. Graham (R-S.C.). (Melina Mara — The Washington Post)

The Senate Judiciary Committee unanimously approved the amendment by Sen. Lindsey Graham (R-S.C.) that would terminate the asylum or refugee status of anyone who returns to their home country. Graham introduced the amendment after investigators discovered that Boston bombings suspect Tamerlan Tsarnaev had traveled last year to Russia and Dagestan after his family sought and was granted asylum from Dagestan in 2002.

In the months prior to his trip, the FBI had opened and closed an investigation into Tsarnaev based on tips from Russian authorities.