What will be case if buck regulator (TPS62067) load current increases the rated current?
From the datasheet:
"The current-limit comparator also turns off the switch in case the
current-limit of the high-side MOSFET switch is exceeded. After a dead time preventing shoot-through current,
the low-side MOSFET rectifier is turned on and the inductor current ramps down. The current flows now from the
inductor to the output capacitor and to the load. The current returns back to the inductor through the low-side
MOSFET rectifier.
The next cycle is initiated by the clock signal again turning off the low-side MOSFET rectifier and turning on the
high-side MOSFET switch."

Sound like your normal cycle-by-cycle overcurrent limiter. You need to provide oscillograms if you mean your device is not behaving this way.