First and foremost this is a bible term, but it is not a term that eliminates the lost from the ability to respond to the word of God and thus receive the word of God, which is the same as it has been and will continue to be under this covenant, No matter how it is projected about who God is and his abilities, it is he that has established that for the lost, a sinner, one not in the family of God is already welcome.
The Welcome Mat is out to any that will answer the word of God, there are no exceptions in the word of God.
2Ti 3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
Any and all scripture is able to bring to past, the declaration within itself, in the heart of man,
The traditions of men will try to eliminate scripture, or add to, and take away from to fit their own doctrine, but this practice will bring self deception to the individual that holds to any tradition of men.
All scripture's have with in them self the ability to bring to past the declaration of the word. That is faith...
Often it is said in defense of the election teaching, that some are eliminated from the family of God the father never eliminates any one .
It is he that calleth things that be not as though they are and expects his children to do the same, and in his heart all are saved, that is the expectancy of faith according to the sacrifice made for the lost.
It requires two scriptures to establish the will of God on any topic, and yes it is known that some would say have fifty scriptures that say otherwise, that is a spiritual impossibility.
So for the lost here are three scriptures to establish the will of God to the lost.
Mk 16:15 And he said unto them, Go ye into all the world, and preach the gospel to every creature.
Mk 16:16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Jn 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
Jn 3:17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
Jn 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
Jn 3:19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
2nd Cor 5:17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.
2nd Cor 5:18 And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation;
2nd Cor 5:19 To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.
2nd Cor 5:20 Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ�s stead, be ye reconciled to God.
2nd Cor 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
2nd Cor 6:1 We then, as workers together with him, beseech you also that ye receive not the grace of God in vain.
2nd Cor 6:2 (For he saith, I have heard thee in a time accepted, and in the day of salvation have I succored thee: behold, now is the accepted time; behold, now is the day of salvation.)