According to WebMD, once a period has started, it is not possible to stop it. However, if a woman starts taking birth control pills, the pills can act to make her period lighter and shorter. Long-term, it is possible for a woman to stop her periods by taking birth control continuously.
The hormones in birth control pills can keep a woman from menstruating. It is not an instantaneous process; a woman cannot start birth control mid-period and expect to immediately stop bleeding.
When a woman has a period while taking birth control, it is not an actual period. Rather, it is a response to the placebo pills that are a part of a standard birth control pack. When a woman takes the placebo pills, her hormone levels drop. The drop in hormones signals to her body to have a period.
If a woman is interested in stopping her period, she needs to skip the placebo portion of her birth control pills and start taking the next pack. There are some birth control pills, such as Seasonale, that are designed specifically to help a woman menstruate less.
Medical professionals disagree about the safety of using birth control pills to stop menstruation for an extended amount of time. Nearly all agree that it is fine to do on occasion. Some doctors argue that a woman does not medically need to have a period, while others believe that the long-term effects of stopping menstruation have not been studied enough for it to be deemed safe.