Is there an operation similar to inset that creates faces in the opposite direction? That is, instead of creating faces inwards, they create faces outwards?
This can be done using the addon "Offset edges".
The simplest solution I have found is by inserting a face as normal.
Then double tab the G key and pressing the Alt key to slide your edge over the border.
Then you can delete the face or extrude it, depends on your demand.