Depending on what you want to do, a workflow might do it. If the field on the form just need to be changed to a set value, you could have the change of that record on the child record update the field on the parent form. However, that won't work if
you're calculating that field from the child records (e.g. aggregate value of opportunities on an Account) without creating a custom workflow step. JavaScript that runs OnSave of the child record will also do, but only if a user working on a form is the ONLY
way the child record gets updated. If anyone ever does bulk updates, updates from workflow, etc., that JS won't run.
The only 100% reliable method that covers all scenarios is to use a plugin that executes when you save a child record. Then it will get executed no matter how the child record is updated.
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