There are some differences between the opera and the myth of Orpheus and Euridice, most notably that Amore (that would have been Eros, to the Hellens) restores Euridice's life despite Orpheus turning to look at her. In the myth, Orpheus must lead his dead wife from the Underworld to Earth without looking back at her. She is so silent, he eventually starts to doubt and just before they reach the Earth, he can't take it anymore and turns around. In the opera, the two haven't even started their ascend yet, when Euridice bewails her faith that Orpheus won't look at her and refuses to move until he does. When he eventually gives in, she dies again. This is where the myth ends, but in the opera, Orpheus' story goes on. Before he can take his own life so he can be with his love, Amore comes and tells him that his love has saved Euridice and she can return to him, and Earth, after all.
I have an issue with the opera adaption; the myth ended with Euridice's death for a reason. Life is for the living; those who die should stay dead or be reborn. Hades rules supreme over the dead and once you are dead, you're done. Amore does not have the power to overrule Hades when it comes to the dying. The dying are dead, as they should be. It's the natural order to things and should be preserved.
The ancient Hellens believed in ghosts; they were the people who could not find the entrance to the Underworld or who didn't have the money to pay Kharon for their passage. Those who were not properly buried were also doomed to wander the Earth for a hundred years. Interestingly enough, Hellenic heroes were also considered ghosts and were honored in the same type of rites as other types of ghosts.
The Ancient Hellens held festivals in honor of ghosts, and the Theoi that presided over them, so they would be sated and appeased and would not haunt them. Most of these festivals included a holókaustos and were solemn affairs, conducted at night and without an offering of wine.
This fear of spirits and other supernatural entities was named 'deisidaimonia' (δεισιδαιμονία). The ceremonies of riddance were known to the Hellens as apopompai (ἀποποπμαί), 'sendings away'. There isn't a single word in the English language that conveys the practice. Closest would be 'exorcism'.
Becoming a ghost was not a good thing. While heroes like Hēraklēs, Theseus and Orpheus head into the Underworld and return from it alive, they never do so without a struggle and the fact that heroes were considered ghosts is food for thought. They have seen the Underworld and have not left the whole of it behind. Ghosts were feared and needed to be appeased, fed with blood to sustain them and/or warded off.
Orpheus looses his wife for a reason; yes, he doubts the word of Hades but more importantly, I believe Hades knew Orpheus was doomed to fail. He knows that those who have good and properly died, need to stay dead. If He didn't, I doubt He would remain an active participant in sustaining the Underworld. Immortality is reserved for the Theoi alone. Those who strive for it, who are not sufficiently pious or simply need to be honored, become ghosts, who wander the Earth without finding rest, warmth or solace. Some, like the heroes, can be petitioned for aid and counsel but the others, the unfortunate souls, are to be feared and 'send away'.
One of the Delphic Maxims is 'grieve for no one' (Μη επι παντι λυπου). Death is a reward in and of itself, especially if you have lived a pious life. Death is not to be feared and those who die, do so for a reason; all mortal life must end, simply because it sets us apart from the Gods. To mourn the dead or fear death itself, is to question both the will of the Gods and mortal thought.