Null character in replacement

sed -e 's/^$/\x00/' replaces empty lines with the a line containing the
null byte.

sed -e "s/^$/\0/" (in bash, an s// expression containing a literal zero
byte) performs no replacements on the stream.

I am not sure if this is simply user error (including error understanding
how bash parses strings before it reaches sed), but I thought I'd report it
in case it was a parsing bug.