Yes. For masked ROMs you can decap the part and read it optically.
Decap is easy for ceramic; you can just break it open. For plastic
packaged parts, it involves fumic nitric or sulfuric acid, so you'd
be best advised to send it to a lab.
Once you can see the die, under a microscope you can distinguish
the one bits from the zero bits. Generally that is the presence or
absence of a metal contact. Whether the presence represents a one
or a zero depends on the specific part number, and might vary
within the array (i.e., it might be presence=1 for the left half
of the array and absence=1 for the right half).
You also will need to determine the layout of the bits. The address
lines are divided into those that address rows and columns. Study
of the decoder circuitry on the perimeter of the array can help
determine this.
If you can take a sufficiently high-resolution photomicrograph of
the die, once you've determined the mapping you may be able to
write software to extract the bits, so that you don't have to do
it by hand.
None of this is easy, but there is an existence proof that it is
possible. Peter Monta optically dumped three ROMs from the HP-35
calculator. These stored 2560 bits each, and were made in 1972 using
ten micron process geometry, The 23256 is a much newer part in
a smaller geometry, which means you'll need better resolution for
the photomicrograph, but it still should be quite possible.
http://www.pmonta.com/calculators/hp-35/
Or you can just buy another unit of the model the 23256 came from.
Eric