Mouth corset
From wipipedia.org
A mouth corset is a type of neck corset that covers both the neck and the mouth. It is popular in BDSM circles because it combines both a neck corset and a gag.
Incorporating a gag into a neck corset does present a few safety issues as should the wearer being to choke it is not easy to remove the gag quickly. For this reason most mouth corsets use a simple muzzle gag that merely covers the mouth and does not force anything into the mouth thus minimising the risk.