Hi Larry,
A very theoretical answer…..
Assuming you could find (or create) a point where the thread is under (more or less) constant tension then it would be possible to sense a break using an optical switch. The output of the optical switch (normally open or normally closed, depending on type or how it’s output is biased) could then be fed into a Mach Input (via your 4 port board) and trigger an event in a similar way that a limit switch halts motion.
Yes, you would have to include some form of safety stop feature before hands were placed within the danger zone but you don’t want to loose position so this has to be carefully thought out. A ‘Feed-Hold’ followed by ‘Stop’ will enable position to be maintained but the only real ‘safe condition’ disconnects all power to the machine (loosing any current stepper motor micro-steps on restoration of power). It all depends on the level of safety you consider is required after fully assessing the potential risk to your well being.

Tweakie.