I'd do it this way:

1. Produce a list of the files into a file using dir /b/s *.xml >yourfiles. (Or your OS equivalent.)
2. Open the list of files with Tie::File; and process the tied array backwards.

   Open each file in turn and then delete it from the array once you've processed it:

   #! perl -slw
   use strict;
   use Tie::File;
   
   tie my( @paths ), 'Tie::File', $ARGV[ 0 ] or die $!;
   
   for my $file ( reverse 0 .. $#paths ) {
   
       ## Open and process $path[ $file ]
       print "Processing file: $paths[ $file ]";
   
       ## Remove the path just processed
       delete $paths[ $file ]
   }
   [download]

To interrupt the processing, just ^C it or kill it or whatever.

The next time you run the program, it will pick up from where it left off, reprocessing the file it was on when it was interrupted.

To continue the processing from a different machine, you only need to have access to the filelist file and script and you're away.