What is the 'work' that may or may not get burned up in 1 Corinthians 3:8-16?
1. Clement of Alexandria says it is “the addition of heresies”.
The Stromata, or Miscellanies - Book V -
CHAPTER IV -- DIVINE THINGS WRAPPED UP IN FIGURES BOTH IN THE SACRED AND IN HEATHEN WRITERS.
"According to the grace," it is said, "given to me as a wise master builder, I have laid the foundation. And another buildeth on it gold and silver, precious stones."
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But "the stubble, and the wood, and the hay," are the additions of heresies.
http://www.earlychristianwritings.com/text/clement-stromata-book5.html
Thus, Clement of Alexandria’s answer to the OP’s question is the heresies of people (not the people themselves).
2. Origen says it is “our sins”:
Origen agrees with Clement that the wood, hay and stubble are NOT people:
DE PRINCIPIIS - BOOK II - CHAP. X.--ON THE RESURRECTION, AND THE JUDGMENT, THE FIRE OF HELL, AND PUNISHMENTS.
4. … Of this fire the fuel and food are our sins, which are called by the Apostle Paul wood, and hay, and stubble.''
DE PRINCIPIIS - BOOK III - CHAP. I.--ON THE FREEDOM OF THE WILL
As, therefore, when a field has brought good and rich crops to perfect maturity, no one would piously and logically assert that the husbandman had made those fruits, but would acknowledge that they had been produced by God; so also is our own perfection brought about, not indeed by our remaining inactive and idle, (but by some activity on our part): and yet the consummation of it will not be ascribed to us, but to God, who is the first and chief cause of the work.
Origen recognizes that in 1 Cor 3, Paul is talking about perfecting ourselves (not burning up previously saved people).
Against Celsus - Book IV -
And we assert that they are wickedness, and the works which result from it, and which, being figuratively called "wood, hay, stubble,"
3. Irenaeus
Book V - Chapter VI -
God Will Bestow Salvation Upon the Whole Nature of Man, Consisting of Body and Soul in Close Union, Since the Word Took It Upon Him, and Adorned with the Gifts of the Holy Spirit, of Whom Our Bodies Are, and are Termed, the Temples.
2. Whence also he says, that this handiwork is "the temple of God," thus declaring: "Know ye not that ye are the temple of God, and that the Spirit of God dwelleth in you? If any man, therefore, will defile the temple of God, him will God destroy: for the temple of God is holy, which [temple] ye are." Here he manifestly declares the body to be the temple in which the Spirit dwells. As also the Lord speaks in reference to Himself, "Destroy this temple, and in three days I will raise it up. He spake this, however," it is said, "of the temple of His body." And not only does he (the apostle) acknowledge our bodies to be a temple, but even the temple of Christ, saying thus to the Corinthians, "Know ye not that your bodies are members of Christ? Shall I then take the members of Christ, and make them the members of an harlot? " He speaks these things, not in reference to some other spiritual man;
Irenaeus recognizes that Paul is talking about burning/destroying that which is within us (sin) not burning up someone else in the 1 Cor 3 passage.