This can be stated in active form. Alternate translation: "Cause his children to be cut off" or "Cause his children to die" (See: [[rc://en/ta/man/translate/figs-activepassive]])
Here the idea of there being no one to carry on the family name is spoke of as "their name being blotted out." Alternate translation: "may there be no one to carry on his name" (See: [[rc://en/ta/man/translate/figs-metaphor]])