"I hope this question makes sense.."

Not nearly as much as I hope the answer I'm about to type makes sense.

First, for most modern day engines, "open loop" insofar as controlling the A/F mixture, is not really.

With the engine idling or just cruising along at a relatively constant speed, "lightly loaded", the A/F mixture is controlled, fully optimized for lowest emissions, via the upstream oxygen sensor(s). When you depress the gas pedal enough, or start up an incline, requiring a level of torque that the engine cannot easily supply absent enriching (~12:1) the mixture, the engine A/F control switches over to MAF/IAT sensor module control, "open loop" only insofar as optimization of emissions level is concerned.

I'm not sure which A/F mixture feedback control loop might be appropriate when the ICE isn't running, or is stopped after running for some period. Perhaps the engineers simply ignored the issue and let the system remain in the previous feedback mode. Or since, seemingly, it matters not at all it may be purely random when the ICE isn't running, stops.

On the other hand if the ICE is not run for a fairly longish period the catalyst may not be up to operational temperature. In that case when the ICE is started, does restart, it would undoubtedly run in enriched, "open Loop" mode even while "idling".

Confused..??