Yes, Penelope remained a faithful wife to Odysseus while he was away. Despite the large amount of suitors, Penelope never betrayed her husband. They remain with her for all of Odysseus' journey, but she always finds a way to put them off until a later time. Her biggest ploy was telling her suitors that she would only marry one of them once she had finished weaving a shroud for Laertes, who was Odysseus' father. For three years, Penelope spent her days working on the cloth and then unraveled her work every night. It was not until one of her servants revealed the secret to the suitors that she was forced to finish it. After it was finished, she told the suitors that she would only marry the one who could string Odysseus' bow and shoot an arrow through twelve axe heads. Odysseus was the one who completed the task, so she was not obliged to marry any of her suitors.