Since the ancient Greek era, being a saint was prohibited to any woman other than Athena herself, and as such, when a woman decides to become a saint, she renounces her gender and covers her feminine face with a mask. Traditionally, it is considered a terrible humiliation for a female saint to be seen without her mask, and if a man sees her face, her only two options are to kill or to love whoever did so. Ophiuchus Shaina (shown to Pegasus Seiya) and Chameleon June (shown to Andromeda Shun) are two examples of female saints who showed their faces (intentionally) only to those they loved (although in Shaina's case, the love was developed after her face was seen for the first time).
Outside of canon
In the Toei Animation series, the saints were said to originally be all male and that no woman had any right to be a saint either with or without a mask, but that the change of times eventually led to the addition of females to the ranks of Sanctuary.
There have been examples of saints who renounced that tradition, such as Aquila Yuna, Gemini Paradox, Gemini Integra and Crane Yuzuriha (who originally abandoned the mask only in the presence of Unicorn Yato and Pegasus Tenma, but eventually stopped wearing it altogether). Saintias are a special group of elite female saints that serve directly under Athena, and are exempt from wearing masks.
Once someone begins the training to become a saint, they may not leave the training grounds without permission of the Sanctuary. Attempting to escape is punishable by death by the hands of any saint or soldier (although in many cases, as with Pakia, saints end up persuading the apprentices to turn back). One may however abandon the claim to a cloth, in which case they cannot abandon servitude, but can choose to serve Athena in another manner, such as a soldier, guard, saint aide or any other occupation that may help the pope and Sanctuary.
The wielding of a cloth
As pointed out by Taurus Aldebaran as he was assaulted by Tanngrisnir Heracles, a saint (especially a gold saint) is also not authorized to wield the cloth to settle personal scores, and may only do so in the name of justice or Athena. A tale speaks of "evil spirits" capable of killing the to-be wielder if he/she opens a pandora box without a good reason, and it serves to assure the uphold of the law in usual circumstances.