If the files are not on an external website, you could try making an ajax request for each file. If it comes back as a failure, then you know it doesn't exist, otherwise, if it completes and/or takes longer than a given threshold to return, you can guess that it exists. It's not always perfect, but generally 'filenotfound' requests are quick.
var threshold = 500,
successFunc = function(){ console.log('It exists!'); };
var myXHR = $.ajax({
url: $('#checkme').attr('href'),
type: 'text',
method: 'get',
error: function() {
console.log('file does not exist');
},
success: successFunc
});
setTimeout(function(){
myXHR.abort();
successFunc();
}, threshold);