Ignoring the error checking you didn't do, my solution is not that much longer than yours (15 to 12), and I'm sure I could lose three lines by combining statements as you did. I think it could be shortened by combining the searching for the marker and the 16 bytes, but I kept it straightforward.

Two differences:

• I didn't assume the trailing "\0\0" couldn't be the start of another message.
• I work on much bigger blocks, which *could* be much faster.

By the way, couldn't
$_ = substr $_, $tiny_read if length > $tiny_read;
be written as
$_ = substr $_, -$tiny_read;
Then you could combine it with the following statement
$_ = substr( $_, -$tiny_read ) . <>;