We're debating over the definition of "failed".
If an O2 sensor isn't sending CORRECT information, I say it's failed. Lazy = failed.
If an O2 sensor isn't sending ANY information, you say it's failed.
My 88 K1500 would set a "lean" code at highway speed. I had adequate rich/lean indication up to about 55--65 mph depending on load/wind direction. Good cross-counts at idle and off-idle, cross-counts reducing as the speed increased. I went nuts on and off for two years trying to figure-out why the truck went lean on the highway. Fuel pressure was good, AIR pump diverted to the air cleaner in closed-loop...and stayed there exactly as designed. Intake gaskets not leaking, no sign of vacuum leaks anywhere.
In desperation, I pulled out the O2 sensor, replaced it with a fresh one. About the same cross-counts at idle and off-idle...but it didn't go lean at higher speed. No more lean codes. Problem solved from that point on. To me, that's a failed O2 sensor. To my shame, I screwed-around now and again for two years playing with injector cleaning, fuel pressure, and re-running all sorts of tests on the emissions controls and ignition system because I didn't pitch a (at that time) $13 one-wire O2 sensor in the trash.
My experience is that a failed O2 sensor will generally report false-lean conditions, driving the computer into rich-command, affecting fuel economy and potentially driveability. I have not seen an O2 sensor fail and deliver rich signal, driving the computer into lean command...but I suppose it could happen.