In the song "Ten Thousand Angels," the last words in the fourth verse states: "Salvation's wondrous plan was done." In the preceding words, He gave himself to die, followed by Salvation's wondrous plan was done gives the idea that there was nothing left for Christ to do in order for salvation to be accomplished. However, Christ was buried, but more importantly, he had to rise from the dead, his resurrection was vital, for without his resurrection he would be as any of us who die. This song is sung by many on Lord's say worship, yet for myself, I've never heard this questioned whether the last verse should be left off when singing.
This reminds me of the second verse of "Amazing Grace" that implies "the hour I first believed," as some teach, you believe and your saved; yet, within the church, it is still sung. I am just thinking about some songs and why the church song leaders don't pay better attention to the words and leave out some verses, which would not be scriptural. For myself, I don't sing that verse, when it's chosen in worship.
In a song, a writer has limited words to express a thought, which often does not allow elaboration upon. Instead, many writers aim to invoke images of events or allude to passages that give greater light on the topic at hand.
Salvation did come by Jesus' death on the cross: "Much more then, having now been justified by His blood, we shall be saved from the wrath of God through Him. For if while we were enemies we were reconciled to God through the death of His Son, much more, having been reconciled, we shall be saved by His life" (Romans 8:9-10). Also while talking about the salvation of both Jews and Greeks, Paul mentioned, "and might reconcile them both in one body to God through the cross, by it having put to death the enmity" (Ephesians 2:16). Yes, Jesus' resurrection also plays a critical roll in our salvation, but it does not mean his death was not important. Notice in Paul's quote, we are justified by His blood, reconciled by his death, and will be (future) saved by his life. The wording in the song is correct, even if it isn't able to tell the full story. In fact, the topic of the song is to remind us of the suffering and death of Jesus. There are other songs that speak of the role his resurrection played in our salvation. The last statement of the chorus is "He died alone for you and me." It is a reminder of "He who did not spare His own Son, but delivered Him over for us all, how will He not also with Him freely give us all things?" (Romans 8:32).
The song "Amazing Grace" states: "How precious did that grace appear the hour I first believed!" The author is merely stating that he appreciated the value of God's grace from the time he first came to believe in God. It doesn't state what the author did in response to that belief. He could be saying that, like the Philippian jailer, he responded immediately to the offer of salvation: "And after he brought them out, he said, "Sirs, what must I do to be saved?" They said, "Believe in the Lord Jesus, and you will be saved, you and your household." And they spoke the word of the Lord to him together with all who were in his house. And he took them that very hour of the night and washed their wounds, and immediately he was baptized, he and all his household" (Acts 16:30-33). In fact, the use of "hour" appears to be a purposeful reminder of the jailer.
No song is a complete message and to expect it is doing injustice to every song. The question is not whether we can find some way to misunderstand a song's intent, but whether a song can be understood in a way that matches the teachings of the Bible.