Would you be willing to accept lower salary if the life in that city had lower cost of living?
That's going to depend entirely on the person.
Regardless of lower cost of living, some people have fixed costs they cannot reduce. Things like student loans, medical expenses, dependents, etc.
Just because AVERAGE cost of living is lower doesn't mean YOUR cost of living will be lower. Theoretically it could increase. Maybe rent is cheaper but mortgages are more expensive.
Once you move to a cheaper place which pays less you are unlikely to have adequate resources to return to a more expensive place to live later on.