> 2)A subscription outside of a invite transaction.
>
> So my query was regarding that BYE which will be sent by a 
> subscriber for a non-invite transaction.

BYE is only applicable to INVITE usages.  Thus BYE should not be sent unless 
sender thinks there is/was an INVITE usage it is attempting to terminate.


> If in this scenario the notifier sends a 481 response, the 
> subscription and the subsequent dialog will be terminated 
> in the subscriber,

If BYE 481 received, it has no impact upon subscribe usage.


> however the subscription will exist at the notifier which 
> on timer timeout will send subscription terminated, on the 
> receipt of which the subsciber will send a 481 subscription 
> does not exists.
>
> Am I right in this regard?

Only if sender of BYE thought there was only an INVITE usage when sending BYE 
and sender of BYE 481 thought there was only a SUBSCRIBE usage when sending BYE 
481.


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