Does God Forgive The Unrepentant?

Does God forgive the unrepentant?
I just came back from a men's camp. The presenter wanted to assure everyone that God WILL NOT forgive anyone that does not repent.  "God can't forgive you unless you are repentant" is actually how the speaker put it.  Can't ?  You mean, as in, Can Not ?  Weird.

Although it's weird to my ears, it is, unfortunately, not uncommon. The "righteous" who have repented (or think they have) do not very much like the idea of God forgiving anyone who has not been as diligent in their spiritual walk and seeking as they have.

1.  Can't God do anything He wants to do?  Who are we to limit God?

2.  Wouldn't God the Father do as Jesus requested?

"And when they came to the place called The Skull, there they crucified Him and the criminals, one on the right and the other on the left. But Jesus was saying, 'Father, forgive them; for they do not know what they are doing.' " Luke 23:33-34

According to some preachers, God would have to respond to Jesus:  "No Way !  They are not repentant, I CAN NOT forgive them... sorry about that son, but I have to work within the theological framework I've set up."  Or, maybe, some would explain it this way:  Yes, God forgave them that particular sin (killing Jesus), but he damned them to hell because of all the other sin in their lives - the sins they had not repented of.  Can you imagine the judgment seat proceedings?  ....Mr. Pharisee, I forgive you for crucifying my only begotten son, but I damn you to hell because you never repented of your other sins, nor did you ever testify to having faith in my son. Goodbye.

Better questions may be: Can God restore an unrepentant person? Does God give assurance of forgiveness to an unrepentant person? Can an unrepentant person be useful in building God's Kingdom on earth?

If these questions challenge your thinking, or your hard-wired paradigms, very good. I don't think it is very healthy to possess a cookie-cutter faith.