Rules, User registration, loop through other users with condition, set field value to 0
Assuming your Rules event is User Updated and you don't have hundreds / thousands of users referencing each of the nodes, 

Use the Action: Fetch Entity by Property [User&gt;Entity Reference Field] and give it the Entity Reference of the Updated User. This will give you a list called Entity Fetched.  


Create a Loop using Entity Fetched  
Add an action to the Loop (on the right) and Set a Data Value: [List Item&gt;Field&gt;Not Current Owner]
Under the loop, Set a Data Value: [Updated User&gt;Field&gt;Current Owner]


That will save each user that references the node. 

If you don't want that because of performance etc., 


You would create a Rules component and send each List Item in Step 2 above. 
Then in that rule component, have a condition that checks the user's Current Owner field is set to True, and have an action to set it to false.
Do step 3 as above in the main Rule to set the current user as owner.