I don't see as it's possible as presented, obviously the lines can be either high or low depending on the signal - so there's nothing you can check there.
Are the two systems microcontrollers?, and are you writing the software for them?.
By having a pullup resistor on the receive side of each line, and holding all the output lines low, you could check that the receive side lines are all low - a break in any wire would result in that line going high.
Or you could send each data packet twice, with the second one inverted, like this - '0010' then '1101'. You could then detect any faulty lines.
Or you could send send pulses on each line, where one type of pulse is a zero, and another type of pulse is a one (using either different frequencies or mark/space ratios) - obviously a missing pulse would signify a broken line.
A lot really depends on what's happening, and how fast it needs to work, plus what control you've got over it all!.