Your'e right-- the "latching" shouldn't cause device destrucion. In fact, positive feedback is used for hysterisis, and that would in fact make this a "flip flop" device (only when there is a dual supply to the amp). Here's the scenario, as best I can understand it:
When the input voltage at the inverting terminal reaches a certain point negative, the output of the amp sends back at positive signal that causes the output to latch "high" by feeding back through the resistor, into the non inverting input. At some point if the input signal at the inverting input goes to a certain point positive, the output of the amp goes negative, and the the device latches negative.
The problem is that this only works when the amp has a dual supply voltage. If there is only a single supply, the device will simply latch positive, when a low enough signal at the inverting input applied. Since there is no way for the amp to amplify negative signals with a single supply, it's probably just going to "latch" high. Some of the newer amps probably don't do that, because they can go perfectly rail to rail. All my experiences with early (741, tl0982, 1458) op amps and positive feedback on a single supply were pretty frustrating, as I can recall. I'm not really all that sure I was doing everything else right in these circuits either and would like to know anyone else's experiments.

Thanks again, Rich

 

Hi,

There's still a question. This looks like it's supposed to be an analog computational circuit - or at least a signal mixer. Is it the case that U1 is incorrectly drawn and labelled? If not, then the circuit is an exercise in futility.

 

I think if the context of the question is purely on/off (digital signals), then there would be a boolean expression-but I'm really bad at them. I kind of tend to agree with Pebe in that the top op amp could be a kind of flip flop, depending on the type of clock pulse and edge trigger and all that. It seems something like W=((-Y+-Z)+X) MIGHT then be true. (?)
Rich