Such an assignment has to end somewhere (semicolon, block end, EOF) to be syntactically correct.
For sake of simplicity, assuming it is really just a comment (as opposed to production data), right on the same line, as in
$comment = <<'EOC'; bla bla EOC
And while you are on it you can even give perl a hint that it can forget about that content as soon as possible:
$comment = <<'EOC' if 0;
Of course, whether you should resort to such "comments" is a completely different question.