Scholarship is still divided on whether Penelope is an agent or a subject. In a famous passage in book 19, Odysseus (still disguised as a beggar) compares his wife's kleos to that of a good king under whom both human society and nature prosper and flourish. Penelope, however, is the first to refuse the attribution of kingly status, her arete and beauty were destroyed when Odysseus left for Troy, if and only if he were to come back to protect her, her kleos would be greater and nobler. It is worth pointing out that Penelope talk of kleos only when referring to herself and her husband jointly, but of arete when referring to herself alone. She does nothing but reinforcing the conventional gender roles.
In a famous article, the scholar Helen Foley highlights Penelope's supposed 'kingly function', which consists in getting gifts from the Suitors (for the purpose of renewing the wealth they are slowly eating away) and goes as far as to claim that she takes on the dissolution of quarrels (also a kingly function). But both these actions are not actually very successful, and make more sense if we see them as clever teasing aimed at stalling the Suitors. Can flirting be considered as active a role as administering justice or managing the household? But if the latter two are the functions Penelope is performing, why do both she and her family constantly complaining that the Suitors are making their own laws and laying waste to the house of Odysseus? Clearly, she is not very successful in her attempts to take control of the situation.
However, she does seem to be much more active when it comes to preventing the suitors from actively taking over the house, by being extremely subtle in their seduction. One famous example is the trick of the web: having promised the Suitors that she would marry one of them when she had finished weaving a funeral shroud for her father-in-law Laertes (an action which has the effect of showing her in a very positive light too), every night she undid the weaving she had completed during the day – which kept the Suitors at bay for three whole years.
If we accept the ambiguity of how much Penelope has been doing to keep the suitors' interest alive, we cannot but conclude that she does indeed play an extremely active role in the Odyssey. Being extremely clever, she never makes that final step (i.e. being unfaithful to Odysseus by marrying one of the Suitors) which would have brought ruin to her and destruction of integrity of the household. In this sense, she truly is the wife of Odysseus – which of course is a total re-establishment of conventional gender roles which see the wife as more of an extension of her husband than a person with her own merits and demerits.