I've had emergency issues twice.
First time I was running near my house and got hit with a crap pain almost exactly a mile from my house. I tried to slow down and make it home. Things were getting worse so I picked up the pace hoping I could make it home. No dice. I had to sneak behind an electrical box on a fairly busy road to handle the business. I was using an app called Vima at the time to track my runs and it would show your route in different colors based on your pace. It was hilarious to look at my route go orange as I slowed down, green as I tried to rush home, and finally a red squiggle while I hid behind the box and took a shame dump.
Second time I was in DFW staying with a friend. Drove from his place in Southlake to white rock lake to run. I realized I needed a pit stop on the way to the lake. Stopped at a whataburger on the way but the door was locked as it was about 4:30am and the dining room was closed. Next door there was a McDonalds so I drove there and had the same issue. Tried to get into a Burger King and it was closed too. Every stop tested my intestinal endurance and the penguin walk to the door and back made things worse and worse. I ended up having to pull up next to an apartment complex with big patch of oleander bushes for me to hide in. Got done and was just about cleaned up when two folks came walking by. I tossed the fast food napkins in the bushes when they were about 20 feet away, jumped in the truck and sped off. I think they were confused about what I was doing but I know they must have figured it out if they kept their course and walked past the mess I made!