If she is not spayed, I guess it is possible she is having a uterine problem such as a miscarriage of a dead embryo. Brown might mean blood or it might mean tissue, if you are sure it is not poop.
Oh, a much more common thing to find in that area is tapeworm segments. I didn't think of it because you said it was brown, and they are described as being like pieces of rice. But I've seen some that are brown.
You could take a stool sample to the vet to check for tapeworms.