Is It Possible for Someone to Lose Their Salvation in Jesus Christ?

In scripture, we're confronted with the reality of people who profess their faith in Christ and fall away. They defect and turn away from Christ. The classic examples are Judas and Demas. 

The problem is, what do we do with these people, and what does it mean for me? Can I have an assurance of salvation, or is salvation something that can be lost?

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