The hymen can be damaged when the cup is inserted. It is good to know that the hymen is not a closed membrane, otherwise the menstrual fluid would not come out either. The hymen is an edge or thickening of the vagina. In every woman this is different, sometimes it is a jagged edge and sometimes a bit smoother. When you insert the cup there can be a tear in the edge, which can cause bleeding. In some cases, this tear can heal and close again. Also, during sports, self-explorations, tampon use, etc. the hymen can be damaged.
In some countries, cultures or religions the status of the hymen is valued and related to the woman's virginity. However, being a virgin is not defined by the state of your hymen, according to medical standards a person is a virgin until they engage in penetrative sex.