I'm ashamed to admit that I should know the answer to this question, but I'm blanking....
In popular tools like ETAP, when I plot inverse time current curves, why does the curve cut-off in the inverse time (long time) region? [top left side of the curve]
Because there's a current below which the device does nothing. There's then a range of currents right above pickup anything other than a numeric relay will have a wide range of operate times. Back in the day, the EM relay manufacturer's wouldn't even try to define performance below 1.5 times pickup.
I’ll see your silver lining and raise you two black clouds. - Protection Operations
Even today, Schweitzer's curves don't start until 1.5X pickup - just like the old electromechanical relays. Unless they've changed recently. It's frankly ridiculous. But as David says, between the pickup current and wherever the curve starts is officially "undefined". If you draw a straight line from the pickup current to where the curve start, you'll be close. But then again, no one is usually going to be trying to coordinate between two overcurrent devices at 800 seconds. That would be pretty rare.