What is "^@"? If it is a Control-@ (ASCII null) character, then
    $string =~ s{ \c@ \z }{}xms;
will do the trick. If there may be more than one, use
    $string =~ s{ \c@ + \z }{}xms;

>perl -wMstrict -le
"my $string = qq{ab.cd\c@};
 print qq{'$string'};
 $string =~ s{ \c@ \z }{}xms;
 print qq{'$string'};
"
'ab.cd '
'ab.cd'

>perl -wMstrict -le
"my $string = qq{ab.cd\c@\c@\c@};
 print qq{'$string'};
 $string =~ s{ \c@ + \z }{}xms;
 print qq{'$string'};
"
'ab.cd   '
'ab.cd'
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