"Traditionally, grammarians frowned on alldanglers, but during the 20th century they generally loosened the strictures for participial constructions at the end of a sentence. Early-20th-century grammarians might have disapproved the following sentences, but they have long been considered acceptable--e.g.: 'Robert stepped to the door, seeking his companion.'/'Tom's arm hung useless, broken by the blow.'
Usually, as in the first of the two examples just quoted, the end-of-the-sentence dangler is introduced by a so-called coordinating participle: seeking is equivalent to and sought. . . ."
- A Dictionary of Modern Legal Usage 246 (2d ed. 1995) by Bryan A. Garner