function someFunction(url){
    $.ajax({
        url: url,
        success: function(data){
            if(data.status == 'FAILED'){
                //Need this ajax to stop
            }
        }
    });
}



$('some-button').on('click',function(
    var url = 'server-url';
    someFunction(url);
));

function someFunction(url){
        $.ajax({
            url: url,
            success: function(data){
                if(data.status != 'FAILED'){
                    //Need this ajax to stop
                }
            }
        });
    }

var req = $.ajax...
..
req.abort()

var ajaxReq = null;
ajaxReq = $.ajax({
        url: url,
        success: function(data){
            if(data.status == 'FAILED'){
                //Need this ajax to stop
            }
        }
        error: function (x, y, z) {
            ajaxReq.abort();
       }
    });