hey
Penelope wants to talk to the beggar because she can do so without compromising herself. Women could not talk to men freely in Ancient Greece unless they were so much beneath them that it was of no consequence anymore. She wants to talk to him because there is something that makes her want to, without her knowing the reason. She hopes he might have some information because her time of waiting for her husband is over,she cannot draw her decision out any longer.
She is desperate and hangs on to a straw. Very human.