I can relate to few experiences of having an accident without diapers... one was when I was in elementary school and one when I had my own apartment (and I was wearing diapers from time to time, just not THAT specific day).
When I was in elementary school, I was around 8 or 9 years old. I had just finished lunch where I drank at least 3 mini-cartons of milk as a dare with the other kids on my table (my classmates). One thing to note: I am lactose intolerant, I didn't realize that until 30 minutes after lunch in the classroom that I had to go to the bathroom REALLY BAD! I told the teacher that I needed to go to the bathroom, and she refused to let me go! She told me that I could wait until the end of the "period". Like hell I could hold off something like that, so I ran off to the bathroom right away, trying to hold in as much as possible. I made it to the bathroom, got in there and pulled my pants down as fast as I could before sitting down on the toilet.
Unfortunately, the explosion started right before I sat on the toilet. Some of them ended up on the floor, a little bit in my underwear and most in the toilet. I was mortified at that point! I ended up staying in the bathroom (or more like hiding!) until the end of the school day because I was too scared to go out there with such things like that happening to me. After I allowed my teacher to come in, I had to clean up my mess. It wasn't fun at all. I learned my lesson to never try drinking too much milk.
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When I was 20, I had my own place where I was able to indulge in my diaper wearing desires, albeit at a limited usage out of the house because I was still afraid of anyone finding out about it - heck, I didn't even know why I liked wearing them, I just did. Anyway, I wanted to eat some lunch at the local Taco Bell one day. I did not have a car, so I had to walk to the restaurant. It was a 10 minute walk, through a small residential neighborhood, and walking between a (mostly) Women college and a hospital to get to Taco Bell. I ate some good food there (well, it tasted good, didn't say it was healthy for me!) and stayed there for 30 minutes before heading back home. Right in the middle of my walk back, I realized I needed to go really badly - and I couldn't really walk back to the restaurant because I knew I would never make it, so I tried to make a mad dash to the bathroom at home.
I had 5 minutes left to get to my apartment so I ran as fast as I could while holding it in. I made it to the house, proceeded to walk up to my apartment, and tried to open the door. Somebody earlier said something about trying to open a locked door while holding it in... I agree with him as it was darn near impossible! As I tried to open the locks, I just couldn't hold it in anymore, I pooped messily while in my khaki pants and underwear. Poor underwear, it had to take so much load that day. I had to tip toe to my bathroom, and I was fortunate to not drop anything along the way. I hopped into the shower afterward - pants and all - to clean myself up. Let me tell you one thing, for such a true accident for me, it felt really good when I ended up losing control of my bowels like that. I know I'm weird, yet it was an exhilarating experience, though it's not something I would want to do again without a diaper.