This may be the dumbest question ever but our customer really wants this. I am asking this silly question just to be sure that it cannot be done.
We have a popup window which has opened by window.showModalDialog (img 1)
In this window there is a custom autocomplete control which displays an html table. The problem is autocomplete table is wider than the modal dialog. So user is unable to see the contents of this table. (img 2)
Then we made initial size of the modal dialog wider enough to see table contents but customer did not want the initial empty area and did not want the content to be wider also. (img 3)
The customer wants to see the thing as in img 4 which i could only made by paint.
Is it possible to display overflowed html content outside the browser. At least for the ones which has opened by window.showModalDialog.
Note: This is about a 10 years old project and it is totally based on window.open and window.showModailDialog. So using a custom jquery dialog or something similar is not an option.

Within your client’s constraints, your task is not possible.
What you could do instead is popup another modal window that shows the contents of the dropdown. That way, you can get a differently sized viewport than what the first modal window offers. Also, if you open the new one as a child, you could even pass messages between the 2 windows.
Of course this will be a very rudimentary stone-age solution! You may also come across a lot of browser limitations/quirks.