If a Christian commits a sin and dies before he repents where does he go?

There is no middle place anyone goes to when they die. The teaching of purgatory by the Roman Catholics is not taken from the Bible, but from their tradition. Each person is either saved or lost. All who are saved go to heaven on the basis of the shed blood of Christ. All who are lost go to hell.

That does not mean that there is no cost for continued or unconfessed sin in the life of the believer. He may lose his rewards. "Look to yourselves, that we lose not those things which we have wrought, but that we receive a full reward" (2 John 1:8Look to yourselves, that we lose not those things which we have wrought, but that we receive a full reward.
See All...). Also, we may be "ashamed before him at his coming" if we are not prepared and ready for the Lord to come (1 John 2:28And now, little children, abide in him; that, when he shall appear, we may have confidence, and not be ashamed before him at his coming.
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However, our place in heaven is not based on our works or on our own righteousness. It is based on the righteousness of Christ applied to our account (2 Corinthians 5:21For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
See All...; Philippians 3:9Thy bow was made quite naked, according to the oaths of the tribes, even thy word. Selah. Thou didst cleave the earth with rivers.
See All...). I may lose my closeness to the Lord, but I cannot lose my relationship as His son. And, it is my relationship as son that determines where my heavenly home will be. God does not have a "dog house" for unfaithful believers.