prevent a function running multiple times after calling it again from ajax

I have been struggling to find a good solution for this problem for a long time. (And I have GOOGLED IT many times). I'm trying to avoid the same function running multiple times when I recall it after an ajax call. I'll give a simple example using the following code:

I load a list of users from my db using php:

while(some loop){
    $users.='
        <div>
            <div>user name</div>
            <div class="replace">replace user</div>
            <div class="delete">delete user</div>
        </div>
    ';
}

And display them inside a div:

<div class="user_wrap">
    <?php echo $users; ?>
    <div id="add_user"></div>
</div>

Now on the front end I can delete or replace each user or add a new user to the div so I run all three functions on document ready:

$(document).ready(function(){
    addUser();
    deleteUser();
    replaceUser();
});

function addUser(){
    $("#add_user").on("click",function(){
        //first load a list of users then select one from it
        $.post("url",{},function(response){
            //add new user to the user wrap
            deleteUser();
            replaceUser();
        });
    });
}

function deleteUser(){
    $(".delete").on("click",function(){
        $.post("url",{},function(response){
            //delete user
        });
    });
}

function replaceUser(){
    $(".replace").on("click",function(){
        $.post("url",{},function(response){
            //replace user with a different user
        });
    });
}

Now the problem comes when I add a new user using ajax I have to rerun both of the deleteUser and replaceUser functions. So thoes functions begin to pile up and can run multiple times in a row. In some cases this is harmless to the result of the function but in some cases it actually harms the result of the function and in adition doesnt it take a lot of system resourses? The only way I was able to prevent it was using Triggers by setting up a global variable and doing some thing like:

DelteUserTrigger = 0;

function deleteUser(){
    if(DelteUserTrigger==1){return false;}
    else{
        DelteUserTrigger=1;
        $(".delete").on("click",function(){
            $.post("url",{},function(response){
                DelteUserTrigger==0;
                //delete user
            });
        });
    }
}

But this mehtod doesnt work as expected it gets the function "stuck" many times as if the trigger didnt change, the on click event just stops responding.

I have also read something about function closure in JS to prevent the same function from running multiple times but I didnt quit understand how to implement that with the ajax call. And is it really useful in this case or am I doing everything wrong here? I would really appreciate some help here.