Always display a picture even if the link is broken?

There’s a PHP function, called getimagesize(), it can do what you’re looking for.

For example:
$url is the image url

$imgsize = @getimagesize( $url ); // @ is needed to prevent error messages

if ( $imgsize       // is the variable is not false
 && $imgsize[0] > 0     // and if the img width is larger than 0
     && $imgsize[1] > 0     // and if the img height is larger than 0
   )
{
    // your file exists, write your code here
}
else
{
    // your file is not available, write your code here
}

If you specify it more, I can make this look better for example into template.