The cross in the Old Testament?

I was in a lecture the other day and Garry Williams was defending the idea that in the Old Testament we see cases where the punishment for one persons sin falls wholly on another and not on the one committed the sin. He helpfully took us to Leviticus 16; Deuteronomy 5:9; 2 Kings 2:26; Lamentations 5:7. I wonder if we can add another...

In Isaiah 39:5-8 we hear Isaiah prophect that: "the days are coming, when all that is in your house, and that which your fathers have stored up to this day, shall be carried to Babylon. Nothing shall be left, says the LORD."

Now I presume this is a judgemnt on Israel for the sins commited at the time of the prophecy or before, but Hezekiah, in his days, will have "peace and security" (Is. 39:8). Is this another example of the punishment deserved by one body being moved to another? Williams says: "that's interesting - I'm making a note to check it out properly when I return to this bit of my research!"