BevelPoly Compound enables you to extrude, outline and inset the provided Poly (TriMesh). It can keep or delete the original surface, which might be used to create only the border quadstrips. The package includes all the compunds it depends on and an example modifier shown in the gif:
Doesn't work on Teapot because of its two-point faces (i.e. faces that only have two vertices, yet still have three edges).
As a bonus, here's another sample modifier (InsetBySelectionValue, see the attached zip file), in this one the inset amount depends on soft selection values: