Hi Ehsan,
The standby supervisor does not mean that the switch is down, the standby supervisor means that it is not working as active switch or router depending on how you have configured redundancy so the l2 modules or the modules in that particular chasiss will still work and be active.
Saying that take an example of HSRP and your 2 cat6k boxes are connected viw a layer 2 siwtch which is connected to the l2 ports on each cat6k box, now one sup in cat6k is active and other sup in second cat6k is standby to decide that hello packets should be exchanged between th 2 switches which will tavel from one cat6k to 2nd cat6k via l2 ports now if l2 ports also go in standby state how will packets be exchanged.
This is just an example so standby sup should not make l2 modules in that chasiss as standby.
HTH
Ankur
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