What I have seen is that the AHJ will often allow a certain percentage of the structure to be rehabbed before having to meet current codes. Say 40% or more of the existing structure would need to be gutted out before current code would have to be met.
Other areas I have seen use a dollar amount, usually also ties in with appraised value of the structure before and after the rehab. I've also seen the AHJ question the intent of the rehab. If the rehabber intends to occupy the structure for a certain time period they go pretty lenient on enforcing new standards. If this is a house flipping project the developer must meet current code at about 20% or so of the appraisal before the project. I've also seen Historic District type organizations have a big say in what can be done & how. The one I've dealt with won't allow anything less than current code and go above code on a ton of stuff. Needless to say this instance ain't cheap.