Hi @Nannette Mori,
I'm pretty sure that it's not possible to do this. At best you could maybe create some scripting rule that was triggered off parent assignment and then validate that the parent was not resolved (and remove the parent link if it was) - but you'd need some 3rd party application like ScriptRunner for this.
Right, so let me take a step back. I'm referring to the issue linking, but you mentioned child issues and the Parent Link, an Advanced Roadmaps' custom field in Jira. Is this the one you are referring to? If so, you will need an app/add-on to help you to achieve this.