Yes, you're correct! In "The Odyssey", the item involved in Penelope's deception of the suitors is a death shroud for Laertes. Penelope claims that she will choose a suitor once she finishes weaving a death shroud for her father-in-law, Laertes. However, every night she undoes the weaving to delay her decision. This deception allows her to buy time and avoid choosing a suitor while waiting for Odysseus's return.
Yes, you are correct. In "The Odyssey," Penelope's deception of the suitors involves a death shroud for Laertes. By promising to choose a new husband after she finishes weaving a death shroud for her father-in-law Laertes, Penelope manages to postpone marrying any of the suitors. Each night, she secretly undoes the previous day's weaving, thus prolonging her deception and avoiding choosing a new husband.