A virgin can only get pregnant if she has sex with someone. But usually this would mean she is no longer a virgin. So are you saying something happened when the virgin in question was having a period that makes her wonder if she was exposed in her vagina to sperm? Because that is what it would take. And, having this occur during a period is not the best time to get pregnant, it's about the worst time to get pregnant. Probably someone in the course of human history who had sex during her period did get pregnant, but it is the least likely time, unless she had sex on the last day of her period and ovulated shortly after. But in your question, the person is a virgin, which would suggest not having sex. (Unless you mean she began as a virgin but then had sex.)
You can get pregnant anytime, typically certain days of your cycle you'll be the most fertile to conceive