Any time someone stop breathing it is called apneas or they apneic. In sleep a chronic condition that may happen is Sleep apneas, which are a group of disorders where some may experience the inability to breath. These can be caused by two things; Obstruction (OSA or obstructive sleep apneas) is where some obstruction usually via muscle relaxation of the tongue or throat causes those tissues to block the airway passage, and nervous system dysfunction (CSA or Complex (or central) sleep apneas) which are caused by the spontaneous stopping of breathing due to stopping of electrical communication between the brain and lungs.
For Sleep apneas two tools are regularity used; a Mandibular advancement device (a mouth piece the pulls the bottom part of the mouth forward, and/or a CPAP (continuous airway pressure machine) which forces airway into the passageways. On an interesting note CPAP is also used to treat those with chronic fluid buildup in their lungs.