Yes women can get pregnant on their period, or at any other time they have unprotected sex. As for most pre not having sperm, i have to disagree as my husband and i used the withdrawal method for years in the 1960s, before we knew about pre ejaculate, yes he pulled out well in time and i got pregnant 3 times. Maybe some guys don't have many sperm if their fertility is low, but that is of no help if you are one guy who has a high fertility count and your girl also is very fertile. Women can also ovulate more than once in one month without knowing, see:-
THE BIG O : Orgasms
It is certainly not worth the risk, to have sex even for a second without protection. if a condom splits or comes off, she should get the morning after pill immediately, it must be taken within 72 hours of the unprotected sex. Also don't forget, no birth control is 100% safe.