Loyalty without evidence
The interesting thing about loyalty in the Odyssey is that it is maintained without grounds. Odysseus has been gone twenty years. Every report of him has been false. Eumaeus says plainly that he no longer believes travellers who bring news, having been deceived before by an Aetolian with a good story.
He keeps faith anyway. So does Philoetius the cowherd, and Eurycleia the nurse, and Penelope. None of them has a reason in the ordinary sense; what they have is a relation to a household.
The division of the house
The poem sorts its household staff carefully, and the sorting does not follow status.
Loyal: Eumaeus, a bought slave who runs the pig farm and performs the poem's best hospitality out of poverty. Philoetius, the cowherd. Eurycleia, bought by Laertes and named with her price. Dolius the old gardener and his sons.
Disloyal: Melanthius the goatherd, who kicks the disguised beggar on the road and later arms the suitors from the storeroom. Melantho the maid, raised by Penelope herself, who insults the beggar and sleeps with Eurymachus. Eleven other women.
Against all of them, the suitors — free, aristocratic, and guests.
The poem's arrangement is deliberate: the people with the least reason to be faithful are the faithful ones, and the men with the most standing are the threat.
What loyalty is paid
The Odyssey is not sentimental about this. When Odysseus reveals himself to Eumaeus and Philoetius in Book 21, he does it with an offer: wives, property beside his own house, and standing as companions and brothers to Telemachus. The loyalty is rewarded, publicly, in the currency of the society.
That is not a criticism of the poem. It is the poem being accurate about a world where standing is the only security a dependant has.
What disloyalty is paid
Twelve women are hanged in Book 22 for having slept with the suitors, and Melanthius is mutilated and killed. The women were enslaved and had no capacity to refuse anything.
The poem presents this as the just punishment of disloyalty. Reading it that way and also seeing that it is the killing of people who could not consent are not alternatives; they are both required, and the poem's own simile — birds caught in a net, feet twitching a little — does not let a reader look away.
Penelope's case
Hers is the hardest kind. Eumaeus keeps faith with a master; Penelope keeps faith in circumstances where faith is indistinguishable from obstinacy, under pressure from her own father and brothers to remarry, with no news, for twenty years, while managing a household under occupation.
Agamemnon among the dead in Book 24 awards her the poem's last word on fame: her kleos will never perish, and singers will make a song for her. He says it in explicit contrast to his own wife.
The Greek terms
Pistis, trust or good faith. Philos, which covers friend, kin and one's own — the loyalty of the Odyssey runs along lines of belonging rather than of affection. Dmōs, the household slave: the word for the people the poem's loyalty mostly comes from.
Later interpretation
The Odyssey's association of fidelity with the lowest-status characters was noticed early and has been read in very different ways — as aristocratic condescension, as a genuine ethical claim about worth independent of rank, and as the household ideology of a society that needed its dependants to be reliable. The text supports argument on all three.