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The term "saved" does not always refer to regeneration/conversion but it can do with their life being saved.
I agree, and that is how it[be saved] is used with the Phillipian Jailor and in Romans 10:9
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead,
thou shalt be saved.
Thats how it is used in 1 Cor 1:21
21 For after that in the wisdom of God the world by wisdom knew not God, it pleased God
by the foolishness of preaching to save them that believe.
Cornelius is an Illustration of this very thing ! That is why God sent Peter to preach to him, to save them that believe, which is the stated purpose !
Acts 15:7
And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us,
that the Gentiles by my mouth should hear the word of the gospel, and believe.
Acts 11:12-14
12 And the Spirit bade me go with them, nothing doubting. Moreover these six brethren accompanied me, and we entered into the man's house:
13 And he shewed us how he had seen an angel in his house, which stood and said unto him, Send men to Joppa, and call for Simon, whose surname is Peter;
14 Who shall tell thee words, whereby
thou and all thy house shall be saved.
There is no doubt that they would hear the word of the Gospel and believe and be saved !
That is the Truth for all the Elect whom God sends the Gospel to as a word of salvation, so they can hear it and Trust and believe ! Eph 1:13
13 In whom ye also trusted, after that
ye heard the word of truth, the gospel of your salvation: in whom also after that
ye believed, ye were sealed with that holy Spirit of promise,
The same pattern with Cornelius To hear the Gospel of his Salvation and believe Acts 15:7
7 And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should
hear the word of the gospel, and believe.
Peter here is saying the same exact thing here as Paul is saying to the Ephesians !