You could be using the word "edit" to mean two things here, so I'll answer both.
If "edit the status" means "change the status to another one", then you are talking about a transition in the workflow. You should place conditions on the transitions you want to protect. A simple example is just to say "only the reporter can use this transition".
If "edit the status" means "edit the issue while it is in status X", then you can apply workflow properties to the status in the workflow to block the editing, or limit it to certain people/groups. See https://confluence.atlassian.com/adminjiraserver071/workflow-properties-802592825.html
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