The Bible says that God never tempts a man to sin, so man is completely responsible for his own sinful actions.
James 1:13 Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man:
14 But every man is tempted, when he is drawn away of his own lust, and enticed.
However, God can use the sinful acts of a person to bring about his purposes. For instance, the children of Israel were forbidden to marry outside their religion, but Samson took a daughter of the Philistines as wife. God used this to deliver the Israelites out from under the Philistines.
Judges 14:1 And Samson went down to Timnath, and saw a woman in Timnath of the daughters of the Philistines.
2 And he came up, and told his father and his mother, and said, I have seen a woman in Timnath of the daughters of the Philistines: now therefore get her for me to wife.
3 Then his father and his mother said unto him, Is there never a woman among the daughters of thy brethren, or among all my people, that thou goest to take a wife of the uncircumcised Philistines? And Samson said unto his father, Get her for me; for she pleaseth me well.
4 But his father and his mother knew not that it was of the LORD, that he sought an occasion against the Philistines: for at that time the Philistines had dominion over Israel.
And I believe it shows in Esther that God can change his plans and adapt to situations.
Est 4:13 Then Mordecai commanded to answer Esther, Think not with thyself that thou shalt escape in the king's house, more than all the Jews.
14 For if thou altogether holdest thy peace at this time, then shall there enlargement and deliverance arise to the Jews from another place: but thou and thy father's house shall be destroyed: and who knoweth whether thou art come to the kingdom for such a time as this?
Mordecai here told Esther that if she refused to go before the king on behalf of the Jews, that God would find another way to deliver them. So I think this scripture teaches that God can adapt to any situation and bring about his purposes regardless of the freewill acts of men.
Another example is Jonah, who disobeyed God's command to go preach to Nineveh and tried to run away. God caused a great storm, knowing the other sailors would cast Jonah overboard. And God had prepared a whale to swallow Jonah which quickly brought him to his senses. But when Jonah first ran away, that was rebellion and sin.
Jon 1:1 Now the word of the LORD came unto Jonah the son of Amittai, saying,
2 Arise, go to Nineveh, that great city, and cry against it; for their wickedness is come up before me.
3 But Jonah rose up to flee unto Tarshish from the presence of the LORD, and went down to Joppa; and he found a ship going to Tarshish: so he paid the fare thereof, and went down into it, to go with them unto Tarshish from the presence of the LORD.
4 But the LORD sent out a great wind into the sea, and there was a mighty tempest in the sea, so that the ship was like to be broken.
Jon 1:14 Wherefore they cried unto the LORD, and said, We beseech thee, O LORD, we beseech thee, let us not perish for this man's life, and lay not upon us innocent blood: for thou, O LORD, hast done as it pleased thee.
15 So they took up Jonah, and cast him forth into the sea: and the sea ceased from her raging.
16 Then the men feared the LORD exceedingly, and offered a sacrifice unto the LORD, and made vows.
17 Now the LORD had prepared a great fish to swallow up Jonah. And Jonah was in the belly of the fish three days and three nights.
So God used Jonah's sin to perform a great miracle which was also a picture of Christ being in the heart of the earth three days and three nights, and rising from the dead.
Matt 12:40 For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth.