At the end of Euripides’ Trojan Women, Hektor’s mother Hekabe (Hecuba) is taken as a servant by Odysseus. Hekabe, however, does not make it back to Ithaka or appear in the Odyssey. What happens?
Apollodorus Epitome, 5.23
“After killing the Trojan men, they burned the city and divided the spoils. Once they had sacrificed to all the gods, they threw Astyanax from the towers and sacrificed Polyxena on Achilles’ tomb. As a reward, Agamemnon took Kasandra, Neoptolemos took Andromakhe, and Odysseus took Hekabê. Some report that Helenos took her and he crossed to the Chersonnese with her and buried her there after she turned into a dog. This place is now called “Dog’s Grave”.
 κτείναντες δὲ τοὺς Τρῶας τὴν πόλιν ἐνέπρησαν καὶ τὰ λάφυρα ἐμερίσαντο. καὶ θύσαντες πᾶσι τοῖς θεοῖς Ἀστυάνακτα ἀπὸ τῶν πύργων ἔρριψαν, Πολυξένην δὲ ἐπὶ τῷ Ἀχιλλέως τάφῳ κατέσφαξαν. λαμβάνει δὲ Ἀγαμέμνων μὲν κατ᾽ ἐξαίρετον Κασάνδραν, Νεοπτόλεμος δὲ Ἀνδρομάχην, Ὀδυσσεὺς δὲ Ἑκάβην. ὡς δὲ ἔνιοι λέγουσιν, Ἕλενος αὐτὴν λαμβάνει, καὶ διακομισθεὶς εἰς Χερρόνησον σὺν αὐτῇ κύνα γενομένην θάπτει, ἔνθα νῦν λέγεται Κυνὸς σῆμα.
This story seems a bit strange, but it is not the only passage that combines a remarkable burial place for Hecuba and Odysseus’ winning of her.
“Dog’s Grave”: Odysseus, once he sailed to Marôneia during the departure from Troy and because he did not agree to leave the ships assailed them in war and took all their wealth. There, because she was cursing the army and making a ruckus, he killed Hekabe by stoning her and buried her near the sea, naming the place the “Bitch’s Grave”.
Κυνὸς σῆμα: ᾿Οδυσσεὺς κατὰ τὸν ἀπόπλουν παραπλεύσας εἰς Μαρώνειαν καὶ μὴ συγχωρούμενος τῶν νεῶν ἀποβῆναι διακρίνεται τούτοις πολέμῳ καὶ λαμβάνει τὸν πλοῦτον αὐτῶν ἅπαντα. ἐκεῖ δὲ τὴν ῾Εκάβην καταρωμένην τῷ στρατῷ καὶ θορύβους κινοῦσαν λίθων βολαῖς ἀνεῖλε καὶ παρὰ τὴν θάλασσαν καλύπτει, ὀνομάσας τὸν τόπον Κυνὸς σῆμα.
Why did Hecuba turn into a dog?
Scholia to Lykophron’s Alexandra, 1176. 14-17
“They say that Hekabe was a witch and a follower of Hekate and for this reason, even if they are speaking nonsense, Hekabe turned into a dog when she was killed with stones. They also say that black, frightening dogs accompanied Hekate.”
ἑπωπίδα δὲ καὶ ἀκόλουθον τῆς ῾Εκάτης φησὶ τὴν ῾Εκάβην, ὅτι, καθάπερ ληροῦσιν (13128), ἡ ῾Εκάβη κύων γεγονυῖα λίθοις ἀνῃρέθη· καὶ τῇ ῾Εκάτῃ δέ
φασιν ἕπεσθαι κύνας μελαίνας φοβεράς. (Ap. Γ 1217)
It is not always the case that Odysseus stoned Hekabe:
Scholia to Euripides’ Hecuba 1259.10-12
“The story is that Hecuba was turned into a dog’s shape and then climbed down to the lowest part of the mast or the sailyard. He threw her into the sea and she drowned.”
μυθεύεται γὰρ ὡς εἰς κυνὸς εἶδος μεταβληθεῖσα ῾Εκάβη καὶ ἀνελθοῦσα ἐν τῷ ἀνωτάτῳ τοῦ ἱστοῦ, ἤτοι τοῦ κέρατος, ἔρριψεν αὑτὴν εἰς τὴν θάλασσαν καὶ ἀπεπνίγη.
And some see Euripides’ play Hecuba as anticipating the famous tomb:
Scholia to Euripides’Hecuba, 1271-2:
“The tomb will have your name: You grave, he means, will take your name in popular knowledge. For everyone will call it the tomb of the dog. Asclepiades says that people call it the “Tomb of the Ill-fated Dog”
“An enchanter of form”: Instead of a nickname based on my form, the grave will be named for what I have now or something else you said. As Polymestor predicts. The grave will not be named for Hekabe, but will be known to sailors as the “Dog’s Grave”. Whenever sailors come to that place where Hekabe’s grave is, then they will know they are nearing dry land.”
† τύμβῳ δ’ ὄνομα σὸν κεκλήσεται: ὁ τάφος σου, φησὶν,τὸ σὸν ὄνομα εἰς κλῆσιν λάβῃ. πάντες γὰρ κυνὸς τάφον αὐτὸν καλοῦσι, καὶ ᾿Ασκληπιάδης φησὶν ὅτι κυνὸς καλοῦσι δυσμόρου σῆμα: —A
† μορφῆς ἐπῳδόν: ἀντὶ τοῦ ἐπώνυμον τῆς ἐμῆς μορφῆς κληθήσεται τὸ σῆμα ἧς ἔχω νῦν, ἢ τί ἕτερον εἴπῃς. καί φησι Πολυμήστωρ· οὐ τάφος ῾Εκάβης κληθήσεται, ἀλλὰ κυνὸς σημεῖον τοῖς ναύταις ἐπίδηλον· ὅταν γὰρ ἀπέλθωσιν εἰς ἐκεῖνον τὸν τόπον οἱ ναῦται ἔνθαἐστὶν ὁ τῆς ῾Εκάβης τάφος, τότε γινώσκουσιν ὡς εἰς ξηράν εἰσιν: —A
Schol. to Euripides’ Hecuba 1273.1-2
“Of a wretched dog”: Asclepiades also says concerning the Dog’s Grave that some people call it the “Tomb of the Ill-Fated Dog.
κυνὸς ταλαίνης: περὶ τοῦ κυνὸς σήματος καὶ ᾿Ασκληπιάδηςφησὶν ὅτι κυνὸς καλοῦσι δυσμόρου σῆμα: —B