What happens in this circuit is that the right side wants to deliver 0-10V at currents up to the current limit of the LT3080 (typically 1.4A). This is driven by the voltage follower op amp based on the VSET voltage.
On the left side, what you need to look at are the adjust pin and output pin of the LT3080. The LT3080 wants to drive the output to match the adjust pin. If there is 1V at the ISET point, that puts the output of the voltage follower op amp at 1V. We now have one op amp that is left which is not a voltage follower. With no current through the 1R resistor (and no voltage across it), you end up with the inverting input of this op amp below the non-inverting input and it rails to its maximum voltage. The LT3080 now drives as high as it can, going into dropout.
When you get 1A through the 1R resistor, you now get a 1V drop across it and the op amp balances, driving the LT3080 in a feedback loop to control the current. The output voltage will vary, but that is fine. The right side LT3080 is no longer in regulation and drives as hard as it can, going into its dropout.
I know the LT3080 quite well. I designed it.