So I'm not sure if there's anyway to do this but maybe there's a way to do this w/ a delay pedal or such.

When recording a song I'll sometimes have  two track like a distorted track and clean one recorded separate and when I song shifts the guitar part from the distortion to the clean part I might have the last note of the distorted track ring out as the clean track comes in.  I'm able to do this because I'm recording the two parts separately, however when playing live I don't know of anyway that I could create or mimic that kind of effect.  I feel like there might be a way to do it w/ a delay pedal, or some other pedal but I'm not sure. 

I'm wondering if anyone has an ideas of how to do this sort of thing or have come with any come up with/is aware of any techniques/effects for this sort of thing.

Electro Harmonix has a Freeze pedal that i think would do what you want. 
The Freeze is the one I was trying to think of.

Aside from that, you'll find that some of the better modeling pedals have paid careful attention to "tails" when changing FX. IOW, the note and/or the effect will continue to ring out and decay naturally even after you've switched to another effect or user preset.
monwobobbo got the Freeze pedal the other day and it works awesome! I wasn't sure if it would hold an effect such as distortion if I then switch off another pedal or switch amp channels, but it does so long as the freeze is further down the chain from whatever I want it to hold. And it seems useful for songs where you use it to sustain chords that you're then free to noodle over. Was using it to play Zeppelin's Thank You. I'm happy I got it.