Just close the autocomplete when the dialog is closed:
$("#dialog").dialog({
close: function() {
$('#tags').autocomplete('close');
}
});
See this in action: http://jsfiddle.net/william/3Yz9f/1/.
Update
It depends what you mean by being "general". JavaScript is very much event-oriented. So, initially, you want autocomplete to close when dialog is closed, hence the first part of the answer. Sure you can bind it to some indirect events, such as autocomplete blur or hide (you may need to do a custom event for the hide), but that gives you a bit of risk that they might not be triggered, as they're indirect.
Now you want it to close when dialog is dragged; well, that's not hard either; you can achieve this with the dragStart
event for dialog, but they're two different events, both on dialogs, not autocomplete. I don't see any indirect event on autocomplete widget itself when dialog is dragged.
If your issue is referring to the autocomplete widget by ID, you could use a context-based selector, e.g. use $('.ui-autocomplete-input', this)
rather than $('#tags')
in dialog's event handlers.