Apex class: 
Task
Public class taskTrigger{
public static void Task(){
        for(Task t: (List<Task>) Trigger.new){
             t.Custom_ownerText_field__c = t.OwnerId;
}
}
}
Case
public class caseClass{
    public static void syncTaskOwner( Map<Id, SObject> oldParents, Map<Id, SObject> newParents ){
            Set<Id> changedOwnerIds = new Set<Id>();
            // Identify all Parents that have a changed Owner
            for( SObject parent : newParents.values() ){
                SObject oldParent = oldParents.get((Id)parent.get('Id'));
                
                if( parent.get('OwnerId') <> oldParent.get('OwnerId') ){
                    changedOwnerIds.add((Id)parent.get('Id'));
                }
            }
            
            // Find all the tasks (repeat for Events if required) that are not closed for the parent records that had new Owners
            List<Task> restoreTaskOwner = new List<Task>();
            
            // revert the owner on the found tasks
            for(Task tsk : [SELECT Id, OwnerId, Custom_ownerText_field__c  FROM Task Where WhatId IN :changedOwnerIds AND IsClosed = FALSE AND Last_Assigned_User__c <> null]){
                System.debug('tsk.OwnerId..' + tsk.OwnerId);
                System.debug('tsk.Custom_ownerText_field__c ..' + tsk.Last_Assigned_User__c);
                if (tsk.OwnerId <> tsk.Custom_ownerText_field__c ) {
                    tsk.OwnerId = tsk.Custom_ownerText_field__c ;
                    restoreTaskOwner.add(tsk);
                }
            }
            if(!restoreTaskOwner.isEmpty())
            update restoreTaskOwner;
        }
}

I have created 2 different test classes both has 0% code coverage.
Test Class
Test Class 1:
@isTest
public class TestClass1{
    @isTest
    static void TestM1(){
        Account acc = new Account(Name = 'Test Acc');
        Insert acc;
        Case ca = new Case(Name__c= 'Test', origin = 'web', Status = 'New');
        Insert ca;
        Task ta = new Task();
        ta.Type = 'Email';
        ta.Status = 'New';
        ta.Description = 'Test SA';
        ta.OwnerId = userinfo.getUserId();
        ta.WhatId = ca.Id;
        ta.Custom_ownerText_field__c = userinfo.getUserId();
        Insert ta;
        
        Profile p = [SELECT Id FROM profile WHERE Name = 'System Administrator'];
        User u = new User(ProfileId = p.Id , Alias = 'Test', Username = 'Test', Email='Test@Test.com', EmailEncodingKey = 'UTF-8', LastName= 'Test', 
                          LanguageLocaleKey = 'en_US', LocaleSidKey = 'en_US', TimeZoneSidKey='America/Los_Angeles');
        ta.ownerId = u.Id;
        update ta;
        ca.ownerId = u.Id;
        update ca;
    }
}
Test Class 2:

@isTest
public class TestClass2{
@TestSetup
    static void setup(){
        Account newAcct = new Account(
            Name = 'Test'
        );
        insert newAcct;
        
        Case newCase = new Case(
            Subject = 'test'
            , Status = 'new'
        );
        insert newCase;
        
        Task newTsk = new Task(
            //WhatId = newAcct.Id
            WhatId = newCase.Id
            , Subject = 'Test'
        );
        insert newTsk;
    }
    
    @IsTest
    static void syncTaskOwnerTest(){
        Task[] existingTasks = [
            SELECT Id, OwnerId, Custom_ownerText_field__c , WhatId
            FROM Task
            Where IsClosed = FALSE AND Custom_ownerText_field__c <> null
        ];
        System.assert( existingTasks.size() == 1, existingTasks );
        System.assertEquals( existingTasks[0].Custom_ownerText_field__c , UserInfo.getUserId() );
        System.assertEquals( existingTasks[0].Custom_ownerText_field__c , existingTasks[0].OwnerId );
        
        User[] usr = [SELECT Id FROM User WHERE IsActive = true AND Id != :UserInfo.getUserId() LIMIT 1];
        
        Test.startTest();
        update new Case(
            Id = existingTasks[0].WhatId
            , OwnerId = usr[0].Id
        );
        Test.stopTest();
        
        existingTasks = [
            SELECT Id, OwnerId, Custom_ownerText_field__c , WhatId
            FROM Task
        ];
        Account acct = [SELECT Id, OwnerId FROM Account LIMIT 1];
        system.assertEquals( usr[0].Id, acct.OwnerId );
        System.assert( existingTasks.size() == 1, existingTasks );
        System.assertEquals( existingTasks[0].Custom_ownerText_field__c , UserInfo.getUserId() );
        System.assertEquals( existingTasks[0].Custom_ownerText_field__c , existingTasks[0].OwnerId );
    }
}

Plese let me know if you have any questions.

Thank you in advance!