According to , the constructions in (12) are analogous to "the barbarians destroyed Rome" and destruction needs to assign theta-roles in line with theta-criterion. It assigns "agent" to the barbarians and "theme" to Rome so (i) is fine. The verb "destroy" alone doesn't obligatorily assign theta-role to its subject so (ii) and (iii) is well-formed, too. However, "destroy" must assign a "theme", so (iv) is ruled out.
