$ echo t\\\  | cat -e
    t\ $
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Abigail

Let's try again, trying to keep the regexp anchored at the end:

s{(\\*)(\s+)$}{ if( $1)
                  { if( length( $1) % 2) { $1 . substr( $2, 0, 1) }
                    else                 { $1 }
                  }
                else
                  { '' }
              }e;
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A bit ugly, but I would think it works: keep the first whitespace in the final sequence if it comes after an odd number of \

s{^((\\.|.)*?)\s*$}{defined $1 ? $1 : ''}e; works too, but I would suspect it is slower (no, I don't have a benchmark to prove it).

The test again:

#!/usr/bin/perl -w
use strict; 

use Test::More qw(no_plan);

while( <DATA>)
  { my( $input, $expected)= m{^'(.*?)'\s*=>\s*'(.*?)'};
    #(my $trimmed= $input)=~ s{^((\\.|.)*?)\s*$}{defined $1 ? $1 : ''}
+e;
    (my $trimmed= $input)=~ s{(\\*)(\s+)$}{ if( $1)
                                              { if( length( $1) % 2) {
+ $1 . substr( $2, 0, 1) }
                                                else               { $
+1 }
                                              }
                                            else
                                              { '' }
                              }e;
    is( $trimmed, $expected, "'$input'");
  }

__DATA__
''      => ''
't'     => 't' 
't  '   => 't'
't\ '   => 't\ '
't\  '  => 't\ '
't\ \ ' => 't\ \ '
't\\\ ' => 't\\\ '
't\\ ' => 't\\'
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