There is no set regulation about this.
However, everyone is required to let INZ know about any new development in their situation while their application is being considered.
And as the last part of the process, the INZ CO will want to interview the applicant about how they are going to fit into and contribute to NZ life. Suppose the CO has information that this person has an application in to go to X country instead of NZ. This is not going to give any confidence that the applicant will be whole-heartedly contributing to NZ.