Most of the newer bizjets do have "emergency descent mode" as an autopilot function. Cabin > 13,500-ish, plane >F250, autopilot coupled, and the A/P does a ninety degree turn off course, throttles idle and speed goes to Mmo/Vmo and levels off at F150-ish. Details depend on manufacturer. On Global Express, EDM can also be manually selected by the crew.
GF