i believe we're held captive by our sin nature. the flesh in which we dwell is in a constant state of sin, either we've just done it, we're thinking about it, or fixing to do it; therefore, we're held captive to sin. i personally believe the very second a soul receives forgiveness & salvation through the finished work of the grace of Jesus Christ is when we're freed from captivity. we still dwell within the flesh until we're granted a new body, but the soul is free from sin(Ephesians 4:30) & our sins no longer hold us captive. we have the holy spirit of God indwelt in us which helps us avoid sin, if we'll heed to the spirit & not grieve it.
or, you could say, we're no longer captive upon death; unless you're a lost soul, then your captivity just went from bad to eternally bad.
myself, i believe it's when you put your trust in Christ & what He did at the cross. one of the first things He did was to go take captivity captive. He took sin to hell & removed the captives.