The shroud is a symbol of female deception. Because she is a woman, Penelope doesn’t have much power to resist the suitors (as seen repeatedly by her son’s commands to go back upstairs to the bedroom, since everything else is a man’s affair). So, since she cannot fight them off or throw them out of her house, all she can do is delay the day she must pick a suitor. So she stretches that out as far as she can by prolonging the time it takes her to complete an honorable feminine task – weaving a death shroud for the despairing father of Odysseus. Though she spends all day weaving, she unravels her work each night. The fact that Penelope does not actually produce the shroud symbolizes her immobility and her helplessness to make any real progress against her enemy suitors.