In Homer's Odyssey, Penelope's situation is somewhat precarious, and may even be an issue of life or death for her, and especially for her son.
Odysseus is the king of Ithaca, but it seems likely that he is dead. Therefore, there is keen competition to replace Odysseus as king. The suitors feel that marrying Penelope will give them a leg up in the competition to be the next king. Meanwhile, Penelope is playing with the suitors. Not only is she fooling them by unraveling the shroud she is making, but she is also taking huge gifts from them.
This makes things dangerous in a couple of ways. First of all, there is the danger of civil war if and when she picks a suitor. They have all been giving her lavish gifts and are all very ambitious. In case of a civil war, someone might well kill Penelope and Telemachus to remove them as a source of power for a rival. Second, if Penelope does marry someone, Telemachus is in grave danger because the new king would likely want to kill him so that the new man's own sons could inherit the throne.
In these ways, Penelope and her son are in a dangerous situation.