unity3d in edit mode can read xml, published as a web mode can not read and why?
Because webplayers have no local file I/O due to security restrictions (or at least that's what I assume you're doing given that you didn't provide any details).
This is a security issue, like Flash the unity webplayer needs to have policy files. The editor is not bound to the security restrictions of the webplayer.
You most probably need to have a crossdomain.xml in the root of the webdomain you are trying to read the xml from.
Put this in the crossdomain.xml for access from anywhere:
See this page in the documentation for more information.