Answer by Keith C for Trigger - update Case field based on FeedItem

I suggest code like this:

trigger MyTrigger on FeedItem (after insert) {
    List<Case> updates = new List<Case>();
    for (FeedItem fi : Trigger.new) {
        if (fi.ParentId.getSObjectType() == Case.SObjectType) {
            updates.add(new Case(
                    Id = fi.ParentId,
                    ??? = fi.???
                    ));
        }
    }
    update updates;
}

It checks that the FeedItem is related to a Case and uses the update pattern that does not involve a query.