Who is the thief described in John 10 and what does he steal?
Let’s begin by looking at the passage as a whole:
Notice that in this context Jesus is speaking figuratively (v.6) and metaphorically to make a point. Jesus is not talking about literal sheep or shepherds, nor is He talking about literal thieves stealing things. He is speaking about the Kingdom of God and how Jesus protects believers from all things, including from those who make false claims and attempt to deceive Christ's followers.
First, Jesus says that He is the door, the one way by which we may enter into eternal life. Before Jesus came, there were others who came claiming to be the Messiah, but these false messiahs were merely "thieves" trying to steal Christ's glory. Because they were not truly the Messiah, God's children (i.e., the sheep) did not hear them.
So notice that the thief in this passage is not the Devil. In this analogy, Jesus says that the earlier false messiahs were the thieves. Certainly, these false prophets were working under Satan's direction, but it is incorrect to say that the thief in John 10:10 is the Devil. In fact, it is the one who falsely claims to be Christ.
Secondly, notice that this is not a passage talking about when people die or how people die or if the Devil can cause someone to die or any of those things. This passage is not talking about living or dying at all. To take this passage and use it to support the notion that Satan is taking the lives of children is grossly improper, completely inaccurate, and a woefully ignorant use of scripture. To repeat - Jesus was not talking about anyone dying.
Instead, Jesus was talking about salvation. He was explaining that when the real Messiah arrived on earth, the people appointed to salvation heard His voice and followed Him into eternal life. They followed Him because God's people will always know the truth about God. Others have come into the world trying to deceive people into following them as if they were Christ (these were the thieves), but they could not steal Jesus' sheep. His sheep know Him and will follow Him.