A KE injection car will run without the O2 sensor connected.
You can even remove the ECU - the engine will still run - although you will have no idling adjustment.

The ECU only regulates the mixture control via the EHA judged by the O2 sensor.
It also controls the idle via the throttle position switch, and the throttle position sensor.

The main issues with stalling are the Fuel Pump relay and the Crank Position Sensor.
The crank position sensor has a nasty habit of working properly when cold and then failing when warmed up.

The CPS can be checked by measuring it's resistance at the EZL connector end - do a search and you will find out how to do this.

Coils can fail however when they go it usually means that the engine will not fire up at all.