What does the bible say about illegal drugs and incarceration in jail for drug possession?
The Bible doesn't address illegal drug use, or incarceration for possession of drugs, directly. However, there is a passage that deals with the broader issue of obedience to law, and the responsibility of governments to enforce the laws.
"Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation. For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power? do that which is good, and thou shalt have praise of the same: For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil. Wherefore ye must needs be subject, not only for wrath, but also for conscience sake. For for this cause pay ye tribute also: for they are God's ministers, attending continually upon this very thing." (Romans 13:1-6)
This says Christians are to be obedient to the laws of the land. He goes on to say that God has given governments the authority to punish or reward. Therefore, if one violates the laws against possession of illegal substances, the government may punish one for that.
It is possible for a Christian to be forgiven by God of this or any other sin, if the guilty party shows genuine sorrow for it and determines not to repeat the act (repents). Although God may forgive the sin, the individual may still be held liable for the legal consequences, such as incarceration or fine.
Since I first published this answer, I have found out that the word translated "sorcery" in Galatians 5:20 (the works of the flesh) is the same as our word "pharmacy." In the sense that they were used in sorcery they are specifically forbidden as a work of the flesh.