I get them backwards. Dyslexia.
Either way the O2 is irrelevant when not warmed up.
I tutored college students Chemistry and Algebra that had Dyslexia. My niece has it, but managed to get a PhD in Law and works in contract law for the Pentagon. They told me the biggest problem is how it switches back and forth depending on stress and caffeine levels. etc, and figuring out if they are seeing the normal view or switched view. The equals sign formula stuff drove them nuts...
Some closed loop, open loop chatter seem a bit confusing. At what time does the engine XJ that is do not read the O2 sensor?
1) When the engine temperature is below a certain pre-programed setting.
Living here in the warm South that is less than 2 minutes after sitting overnight.
2) At WOT (Wide Open Throttle) which do not happen often,..at least by most of us.
A few years ago, my XJ delivered a whopping 12 MPG's in totally flat South Florida highways down from 18+. I spent days checking everything on the XJ for leaks. There was none. One day while walking around the back of the XJ with the engine running I was greeted with the over whelming smell of unburnt fuel. A new O2 sensor checked the rapid lightening of my pocket book. The worrying part of the entire ordeal was, nothing was indicated in a scan for codes and thus no check engine light.
Yes, my 1996 XJ killed 2 (two) O2 sensors in almost 200,000 miles and never gave a clue or warning that the O2 had departed the land of the living.
In all my testing, the ECU/PCM was closed loop in under 60 seconds on all my 87-2001 rigs from a cold start. The electric heater element in the O2 sensor heats the sensor up to operating temps very fast. But I have never tested mine at ambient temps on a cold start under about 55 *F here (that I recall).
Up north at -10* F it may take a good bit longer.
I had a Ford
1996 Taurus that could drive all day for days in open loop and never throw a CEL, but was "Thinking about and testing shit as it tried to lock in all the sensor BS, while it had a massive vacuum leak Dangling loose hose) or massive miss from a spark plug wire was that was not connected.
Even the disconnected the spark plug wire never threw a code, because it got everything locked in, never got past the relearn mode. Therefore it could never go closed loop. Never threw a code!!!!
My scanner shows me when the ECU claims to be in closed loop mode. I can actually watch when mine shifts to open loop. My 87 and my 2001 Saturn never leave closed loop except at WOT, right after WOT going to a closed throttle (in park) and during 100% decel / braking operations.
But the ECU is always reading the O2 sensor and trying to go back to closed loop when the O2 sensor finally gets off the Pegged high or low readings and crosses the mid point signal voltage again.
My scanner (Snaop-on MT-2500) says it is staying closed loop during gradual acceleration and gradual deceleration. They may have a different definition of what "Cruise" means in the manuals than I do????? But it switches in milliseconds to open loop when I stomp on the gas pedal in park and rev her up to 4000 rpm in about 1-2 seconds. And about 1-2 seconds after the O2 sensor data goes back to a live reading (not pegged at max on min) the ECU says it is closed loop again. Going from 4000 rpm to idle, 750 rpm, seems to take my Saturn about 6-7 seconds to go back to closed loop. My guess is the EGR slows down recovery of the process on the 2001 Saturn.
Sometimes folks redefine key words from one group to another. Consider what "Cruise" means in "Cruise control" it is not a fixed gas pedal position or fuel rate!!! Also if you try and hold the VSpeed steady, and go from up hill to downhill, the fuel rate and air flow change slowly, that is still closed loop!!! Thus the question is when it is Cruise not cruise,
and when is a lie not a lie, and a crime not crime, LOLOL. 
In summary,
keep in mind the ECU always reads the O2 sensor data.
Then the question becomes, when and why does it do something to try move the O2 sensor reading?
What it does about the reading it sees, and when it does change fuel rates, is a different question!!!
For instance, the ECU will try to get a proper, mid point O2 sensor reading even in open loop and try to force the O2 sensor to switch from high to low or low to high!!!!
So it is trying to switch to closed loop!!!
At some point I think they give up, if they reach a point where they know the sensor or wiring is forked!!!
So I think Open loop has two modes. Pure Open Loop (The I give up, the O2 sensor is dead mode, throw a CEL), and Open-loop trying to switch to closed loop modes.
I think the Open loop trying to switch to closed loop, may sometimes lead lead to RPM hunting, when it can correct of problems like a variable vacuum leak, or.....
One last thing. The ECU/PCM is always operating in a closed loop mode, lets call it Mode 1. Where it runs the engine rich (At least it thinks is). It uses all the input data except the O2 sensor.
Then we have closed loop MODE 2, when it adds the O2 sensor data and tries to meet all the demands and program instructions including the operator gas pedal instructions....as well as tries to hold a steady O2 sensor reading of 2.45 volts AC (Renix) (.45 volts AC HO) by controlling the fuel rate.