Buying a bunch of various size screws is an excellent suggestion.

Otherwise:
Before trying it again, shoot some WD-40 into the recess and let it seep
in for a while; it may help. If worse comes to worst, drill through the
door handle so that you can use the long leg of the Allen wrench to
reach the screw head. Put a pair of pliers on the short end so that
you can simultaneously push hard and turn hard.

Or you could just hacksaw the handle off of the door.

MiamiCuse wrote:
I have a aluminum glass door where the handle is attached to the door frame
via two allen screws. One of them fell out and disappeared so I have to
take out the second one in order to get replacements.

The problem is that the second screw seem to be stripped. The screw is
hidden behind the inside facet of the handle and the entire screw is
threaded, there is not a wider bigger screw head, the screw disappears
completely inside the screw hole.

Now as I tried to unscrew it, it is not coming out, I believe the hex shaped
hole may be rounded, and I cannot get enough leverage to see into it. There
is no room to use any kind of drills or screw extractor at that angle.

Any ideas?

MC