Let's say that at some point after the Norman invasion, England just totally goes balls up, and Scotland takes advantage by moving its boundary to the South. The Borders were always a hazy concept, and North England, especially prior to standardization of English, was pretty much part of a linguistic continuum with the Lowlands. There wasn't really a concept of Anglo-Saxon identity on one side, or "Celtic" identity on the other as of yet either.
Could Northumberland be culturally absorbed into Scotland? Tyne and Wear? Cumbria? Durham? Points even further south like Yorkshire?