IDP to receive an unsolicit authresponse

Title: IDP to receive an unsolicit authresponse

Hi,

I haven't seen this in the profiles but I was wondering whether makes sense for an IDP to receive an 

Auth response from may be another IDP.

I was wondering if there are 2 enterprices (A and B) in a trust relationship both providing 1 IDP (IDP A and IDP B)

If IDP A web portal provides a link to IDP B and I just logged into IDP A and tried to follow the link to IDPB,

Wouldn't make sense for IDP A to send an Authresponse to IDP B ?

Also If I had a link from IDP A to SP B (service provider in B) and I tried to follow this link,

SP B would probably receive an Auth Response from IDP A but shouldn't some how the IDP B be notified about this ?

What do you think ?

Thanks.

Giuseppe.