For JiraPermissionHolderType GROUP what is the difference between "parameter" value and "group"."name" value?

I notice in the API response that for some project permissions returned in the API, for a group permission holder type the parameter value does not match the value in the response. Under what conditions does this happen, and how should the caller determine what is the group referred to?
For instance, in case the permission refers to a group that was subsequently deleted, the value is jira-software-users while the parameter value is the group.