Scripture doesn't address accidents and the like. In the context of Christianity, this means the only valid answer is "We don't know".
The King James and other versions do use the word "perfect" in several places in the Bible when describing saved state:
2 Timothy 3:17 That the man of God may be perfect, thoroughly furnished unto all good works.
Hebrews 6:1 Therefore leaving the principles of the doctrine of Christ, let us go on unto perfection; not laying again the foundation
of repentance from dead works, and of faith toward God,
Hebrews 10:14 For by one offering he hath perfected for ever them that are sanctified.
James 2:22 Seest thou how faith wrought with his works, and by works was faith made
1 Peter 5:10 But the God of all grace, who hath called us unto his eternal glory by Christ Jesus, after that ye have suffered a while,
make you perfect, stablish, strengthen, settle you
The above are just the first few I found, but there are plenty more. However, the meaning in the original language is usually better translated as "Mature", "justified", or "sinless" depending on the context and the original word(s) used. They don't indicate the lack of accidents in the manner you described.