my last post was confusing, so I will summarize it.
The two sons in Matthew 21 received the call to go work in the vineyard. The first son said he would not go, but went. The second son said he would go but did not.
Context seems to indicate that "entering the vineyard" equals entering the Kingdom of God by repenting at the preaching of John. (verses 31-32)
Both were represented in the parables as sons, but not all of them had repented and entered the kingdom of God. The second son did not repent. He did not enter. He did not hear. Yet he is called a son. SO your assumption that the word "son" always has to mean a saved person, ie son by birth, is not correct. It does not always mean that, as seen here.
The Prodigal son parable is very similar to this parable. Luke 15:1-3 strongly indicate that the prodigal represents INITIALLY the publicans and sinners, and secondarily anyone who is sinful and comes to Jesus for salvation, the elder son represents those who grumble at their return.
So, if the prodigal son represents the publicans and sinners, it cannot be said that they began with a starting point of being saved. They were not saved until they came to Jesus. and the prodigal represents one who coming from a life of sin comes to Jesus and is saved. That is how it is always used in the Bible, albeit it is only used one time. SO to ask, "would the prodigal have ceased to be a son if he had died as a prodigal" is a moot question, because NOWHERE in scripture do we see the prodigal son dying in his sins. We see the prodigal is a sinner saved by grace.
And nowhere in scripture do we see the prodigal failing to return, because EVERY place the prodigal is mentioned, HE RETURNS>
Now the scribes and Pharisees, elder son, reaction is left open. They may return or they may not return. Jesus is opening the door for them, will they go through it? Some will and some wont
So it is even today...