Scribe with open and/or intersecting contours?
Here you go.
Make the shape you want to scribe.
Offset it with a proper distance.
Then you need to eliminate those areas that intersects so it's just one open contour by using the trim tool, then we close the ends to make it a closed contour.
Before we can trim the entities we have to delete the offset relations.
Here's the finished sketch with some modification I made. Just a nice closed contour.
Then scribe away.