I, too, have heard the “On My Own” song with new lyrics sung at Catholic funerals and I love it! I couldn't find any recordings of the "hymn" version but here is the original song....
Melody starts around 1:33
Nice that the singer changes the pronoun to him vs her depending on the gender of the person who died … here are the lyrics I was given by a local church musician:
Song of Farewell
(sung to the melody of "On My Own" from "Les Miserables")
Saints of God, o come to his/her aid
Come, o saints, come now that he/she is sleeping
Remember, the Lord has always loved us
Jesus gave His life for us now take him/her to your keeping
Come to me, where chains will never bind you
All your grief at last, at last behind you
Lord in Heaven, look down on him/her in mercy
Forgive her all her trespasses and take him/her to your glory
Take his/her hand and lead him/her toward salvation
Take his/her love for love is everlasting
And remember the truth that once was spoken
To love another person is to see the face of God