Chosen Solution
1999 saub 93 convertible: ignition turned off but radio remains on.
Yup, it’s by design. It’s so that you can keep listening even when the engine is turned off
I suppose the radios power lead is directly wired to the battery current. Find a cable that is triggered by the ignition (e.g. the lightswitch) and wire it to that.
A piece of metal covering over the key hole has maybe been pushed inside the ignition. It causes the car to act as if something has been left on. It does not run the battery down but have to manually lock the doors.
The Saab has an ignition switch in the center section of the transmission/handbrake area. Over time, this gets dust into the mechanism and when the key is removed the ignition no longer pops up. This is a very common problem with Saabs, especially the 93 and 95. You can try jiggling the key to pop it back out. If this does not work, you could also try blasting it with some compressed air and then applying some WD40. Usually that will fix the problem.