TC Electronics calls it 'fx spillover'.......as far as I know it is what happens when you change profiles on the Kemper. I'm not sure 100% but it should be like this since I used it live a lot.
will make some test tomorrow on my rig and will let you know for sure............
anyways, the delay staying when you change the patches has nothing to do with the CC. I think the CC assignment pertains the fact that you can assign a switch to the delay, turning it off thus playing dry having the trail remains until it is completly faded out.
hope this helps
mic
I use a Behringer FCB1010 as Footcontroller for the KPA. When changing rigs the FX spillover works like a charm.
Check the midi section of the manual... it's in there. I can't remember specifically which CC numbers it is, but there are two for switching the delay and reverb, one keeps the trails, the other cuts them.
hope that helps.
the fact is that Jonas mentioned the rig/profile change, not the swtiching on off of the delay with the audible delay trail. as said, apparently Jonas enquire has nothing to do with the CC assignment. the CC implementation for the delay or other effects on/off is useful only when the profile remains the same and I want to cut or add an effect. Jonas wants to change profile and still hear the delay from the previous profile to be audible in the profile he just recalled.
as tyler said, it is what happens when you change profile. to make a suitable test, program a very long delay on a profile and then change to another profile. you should be able to hear the first long delay in the new profile. consider though that the delay trail might be infleunced by the new sound.
mic
Ahh.. ok I misunderstood... apologies 
