This is going to sound very confusing to some. I do not believe a person can lose their salvation. I believe in the Preservation of the Saints, not Perseverance.
But...
The unelect can become the elect through faith.
Before you laugh, here it is in scripture.
Rom 11:7 What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded
8 (According as it is written, God hath given them the spirit of slumber, eyes that they should not see, and ears that they should not hear; ) unto this day.
9 And David saith, Let their table be made a snare, and a trap, and a stumblingblock, and a recompence unto them:
10 Let their eyes be darkened, that they may not see, and bow down their back alway.
11 I say then, Have they stumbled that they should fall? God forbid: but rather through their fall salvation is come unto the Gentiles, for to provoke them to jealousy.
12 Now if the fall of them be the riches of the world, and the diminishing of them the riches of the Gentiles; how much more their fulness?
13 For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
14 If by any means I may provoke to emulation them which are my flesh, and might save some of them.
15 For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead?
16 For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.
17 And if some of the branches be broken off, and thou, being a wild olive tree, wert graffed in among them, and with them partakest of the root and fatness of the olive tree;
18 Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee.
19 Thou wilt say then, The branches were broken off, that I might be graffed in.
20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
21 For if God spared not the natural branches, take heed lest he also spare not thee.
22 Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.
23 And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again.
24 For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
The Jews are God's chosen people, his elect. They are here compared to an olive tree. They are called the "natural" olive tree or branches.
The Gentiles are called the "wild" olive tree or branches.
Here Paul explains that Jews have been broken off of their tree through unbelief, and that Gentiles have been graffed into this tree through faith.
Rom 11:20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
21 For if God spared not the natural branches, take heed lest he also spare not thee.
Now, these verses almost seem to argue that a person can lose their salvation. It tells us the Jews were broken off because of unbelief. Well, didn't they have to originally belong to this tree to be broken off? And then Paul warns us not to be highminded and says if God spared not the natural branches, take heed lest he also spare not thee. However, in verse 7 it says the elect "hath obtained it", which is speaking of God's grace shown in Rom 11:5-6.
And the scriptures say to make our calling and election sure.
2 Pet 1:10 Wherefore the rather, brethren, give diligence to make your calling and election sure: for if ye do these things, ye shall never fall:
Now, this verse flies in the face of Calvinism. If only God determines who is the elect, then why does Peter tell us to give diligence and make our calling and election sure? What could a man possibly do to make his calling and election sure if Calvinism is true? Nothing. I believe this verse is saying to make sure you are truly trusting in Christ alone to save you.
But back to Romans 11, note that these unbelieveing Jews who have been broken off the natural olive tree through unbelief can be graffed back into their own tree again. And that word "again" argues that they were originally the elect, became unelect through unbelief, and can become elect again if they repent and believe.
Rom 11:23 And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again.
24 For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
So, you are not first elected, and then God causes you to believe. No, your election is based on whether you believe or not. And a person who is at this time the unelect through unbelief can repent and believe and become the elect.
I am convinced that the elect are the Jews. But it is a believer that is a true Jew.
Rom 2:26 Therefore if the uncircumcision keep the righteousness of the law, shall not his uncircumcision be counted for circumcision?
27 And shall not uncircumcision which is by nature, if it fulfil the law, judge thee, who by the letter and circumcision dost transgress the law?
28 For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh:
29 But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.