Nothing much. Some of the meals have a high fiber cracker you can use with the Peanut Butter or Cheese Spreads and I think the chocolate drink mix has some fiber. But I don't think it provides nearly enough fiber to overcome the logjam inside you. Eventually it just passes. But the meals aren't meant for long-term survival (no more than a month or so) anyway.

I spoke one time with a researcher who worked for the part of the army that put together the requirements for the MREs and the problem is that getting fiber-full food to stay stable for 3 years is an open problem.

If you really look into the science behind the MREs it's really some amazing technology. There's also some really cool hacks they use to keep the food shelf stable without preservative chemicals. I wish I could find the article about some of what they do.