The 87 190D has 602 engine. I think the vacuum shutoff module is on top of the FI pump like my 603 engine. Remove the vacuum line to the module and look inside the line. If it is oily, the vacuum module is bad. I saw leaking module that still stopped the engine when vacuum applied. When the module is partially leaking and other part of the vacuum system is in good condition, the driver may not notice any problems.
The bottom line is: if the engine does not stop immediately (a sharp stop with no delay) after key is off, you have a problem. It may be a bad vacuum shutoff module, leaking hoses, bad vacuum pump, or the combination of all of the above. I would start checking for oil inside the vacuum line for the module. Replace the module if necessary. If the engine still does not shut off immediately, you have other vacuum related problem(s). Steve provided detailed steps to check vacuum leakage in the following link: