It has never been clearly stated in dialogue what the respiration devices worn by the Benzites were truly used for or what happened to them. Mike Okuda explained the absence of the apparatus in "The Ship" by pointing out "there's been some advances in Benzite technology!" (Star Trek: Deep Space Nine Companion)
Mordock's respiration device was originally conceived as being "a special suit using circulating gas tubes." Mendon's device was later described as being "a special device at his chest which converts the oxygen level to his use."