Hi Richard Stephens,

Please find the solution to your question with 100% Test Coverage.

 I want to tell you that you can get data in trigger.old only when you would update the records. Before insert and after insert there is no data in the trigger.old.

Trigger

trigger AccountTrigger on Account (after update,before update) {
    
      if(Trigger.isBefore && trigger.isUpdate) {
          
        EventUtil.setOwnerIds(Trigger.oldMap, Trigger.newMap);
    }

    if(Trigger.isAfter && trigger.isUpdate) {
        EventUtil.updateOwnerIds();
    }
    }

public class EventUtil {

    /** Event Id => Original Owner Id **/
    public static Map<Id,Id> originalEventOwnerIds = new Map<Id,Id>();

    public static Void setOwnerIds(Map<Id,Account> oldMap, Map<Id,Account> newMap) {
 
        /** Only process this data if the Account (household) owner changed **/
        Id[] changedAccounts = new Id[]{};
         for(Id hhId : newMap.keySet()) {
            if(oldMap.get(hhId).OwnerId != newMap.get(hhId).OwnerId) {
                changedAccounts.add(hhId);
            }          
        }
        for(Event e : [Select Id, WhatId, Subject, OwnerId, Owner.Name from Event where WhatId in :changedAccounts and StartDateTime >= TODAY]) {
            originalEventOwnerIds.put(e.Id, e.OwnerId);
        }
        
    }

    public static Void updateOwnerIds() {
        if(originalEventOwnerIds.isEmpty()) return;
        /** Grab active user list to see if the old user is still active **/
        Map<Id,User> activeUsers = new Map<Id,User>([Select Id, Name from User where IsActive = true and Id in :originalEventOwnerIds.values()]);
          Event[] eventsToUpdate = new Event[]{};
        Event[] allEvents = [Select Id, Subject, OwnerId, Owner.Name from Event where Id in :originalEventOwnerIds.keySet()];
        system.debug('originalEventOwnerIds.get(e.Id)::::'+originalEventOwnerIds.get(allEvents[0].Id));
        system.debug(' e.OwnerId::::'+ allEvents[0].OwnerId); 
        for(Event e : allEvents) {
            if(activeUsers.keySet().contains(originalEventOwnerIds.get(e.Id))) {
                e.OwnerId = originalEventOwnerIds.get(e.Id);
                eventsToUpdate.add(e);
             }
        }

        if(eventsToUpdate.size() != 0) {
            update eventsToUpdate;
        }
 
    }
}

Test Class :

@isTest
public class setOwnerTest {
    
    static testMethod void inactiveOwners() 
    {
        try{
            Profile p = [SELECT Id FROM Profile WHERE Name='System Administrator']; 
            User usr = new User(Alias = 'PC', Email='pc@testorg.com',IsActive=true,
                                EmailEncodingKey='UTF-8', LastName='PcTesting', LanguageLocaleKey='en_US', 
                                LocaleSidKey='en_US', ProfileId = p.Id, 
                                TimeZoneSidKey='America/Los_Angeles', UserName='pc@testorg.com');
            insert usr ;
         
            Account a = new Account();
            a.Name = 'Test';
            a.OwnerId=usr.id;
            insert a;
         
            User usrr = new User(Alias = 'pct', Email='pct@testorg.com',IsActive=true, 
                                 EmailEncodingKey='UTF-8', LastName='pcTestingg', LanguageLocaleKey='en_US', 
                                 LocaleSidKey='en_US', ProfileId = p.Id, 
                                 TimeZoneSidKey='America/Los_Angeles', UserName='pct@testorg.com');
            insert usrr ;
               
            Event e = new Event();
            e.WhatId=a.id;
            e.StartDateTime=system.today()+2;
            e.EndDateTime=system.today()+5;
            e.OwnerId=usrr.id;
            insert e;
            Account ac=[select id,name from Account where name='Test' limit 1];
            ac.name='imtiaz';
            ac.OwnerId=usrr.id; 
            update ac;
       
            test.startTest();
            EventUtil.setOwnerIds(oldMap,newMap);
            EventUtil.updateOwnerIds();
            test.stopTest();
        }
        catch(exception e){
            system.debug('Message:: '+e.getMessage());
            system.debug('Line:: '+e.getLineNumber());
            
        }
        
    }
    
}

Please let me know it is working or not??? please tell

If it helps you please mark it as Best Answer so that other people  would take reference from it.

Thank You!