multiple problems:

• you say "word" but you mean string, right?
• you don't anchor to the end of the string with $ but to the start with ^
• you use an all quantifier * for the negated class, which also means 0-times, so r doesn't need to be rejected and the if-clause is entered.

Actually I don't know any more what your real goal is, so no recommendation other than

  DB<114> $in_str = 'aa<c><d>r';
 => "aa<c><d>r"

  DB<115> if ($in_str =~ /aa((<[^>]*>)*)$/) {print "$1"}
 => ""

  DB<116> $in_str = 'aa<c><d>';
 => "aa<c><d>"

  DB<117> if ($in_str =~ /aa((<[^>]*>)*)$/) {print "$1"}
 => 1
<c><d>
[download]

maybe try to show us better input and desired output.

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