My Euro 16 valve, and according to my manual, your US model have a micro switch on the throttle linkage that shuts down the fuel supply when you take your foot off the gas above something like 1700 rpm, and is supposed to pick it up again when it reaches idle speed. This item can be dirty or stuck causing your problem.
It can also be the "idle motor" which is a device for controlling idle speed as only a German engineer could dream up. It resides between the intake runners for the No. 2 and No. 3 cylinders, is about three or so inches in diameter and about five inches or so long. Its function is to regulate air flow at idle, apparently, and on my car it stopped turning. It has an electric motor inside that spins a drum with an orifice arrangement. When they get old and dirty they can stick. Others on the forum have rinsed them out with carb cleaner and some mechanical agitation and put them back in. I had mine replaced quite a while ago and the new one has been pretty good. When they fail the ability to control idle, especially when the air conditioning compressor cycles, is lost.
Good luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)