It is possible that the toilet paper is disintegrating on your vulva because you are rubbing it too harshly or excessively. It is important to be gentle when cleaning this area. If you try to clean too forcefully, the paper may tear. Once the toilet paper has been used in that area, it should be disposed of and not reused on other parts of the body. To prevent the paper from tearing, you can also try lightly wetting the toilet paper with warm water as an alternative.