/(^.*\z)(?(?{ $+ eq reverse $+ })|(?!))/s

##</code><code>##

/
    (                            # capture group
        ^                        # match begin of string
        .*                       # match everything
        \z                       # match end of string
    )
    (?                           # if
        (?{ $+ eq reverse $+ })  # $+ (last captured group) is palindrome
                                 # then match nothing (succeed)
    |                            # else
        (?!)                     # fail on matching nothing (fail the regex)
    )
/xs                              # x for readability, s to make . match \n

# Note: can match empty string

##</code><code>##

rule palindrome {
    $foo := (\w+) ::: { fail if $foo ne reverse $foo }
}

# Note: doesn't match empty string

##</code><code>##

/(.+)(??{ reverse $+ })/s

##</code><code>##

/
    (.+)                          # match one or more characters
    (??{ quotemeta reverse $+ })  # match the reverse of what was matched
/xs

# Note: doesn't match empty string or single character string

##</code><code>##

rule palindrome {
    $foo := (\w+) <{ quotemeta reverse $foo }>
}