Hi,
I really like the Linear Technology's LT3080 regulator.
I have not used the physical part yet. But I plan to.
The datasheets says that set pin has a 10microamp current source.
Say I had a simple regulator set up as in figure 1 of the datasheet and the resistor connected to the set pin got disconnected.
I am thinking that the output would go to the input rail minus any dropout voltage.
But then I am wondering how the regulator would work with no path for the 10uA to go.
What does the regulator do, let the voltage go up or is there some protection built in to stop this.?

 

Get yourself a copy of LTSpice and do the sim, there is most likely a model in the sim for that regulator.

 

What does the regulator do, let the voltage go up or is there some protection built in to stop this.?

Basic circuit below;
As you can see, the 10μA set current develops a volage across the Rset resistor, which is buffered by the internal op amp non-inverting follower and transistor to generate the output voltage.
So if Rset is open the Set voltage will go to its maximum and so would the output voltage.
There is not anything internal to stop this.

If this is a problem (why) then you could add a Zener across the set resistor, which would clamp the output voltage at the Zener voltage.



Ltspice simulation below:

The two switches, S1 and S2 control the connection of Rset and the Zener, D1 to ground.

With Rset connected (red trace high) the output (yellow trace) is 5V due to the 500kΩ value for Rset.

When Rset it opened by S1 and the Zener is not connected (red and green traces low) the output goes to it's maximum of about 11V with a 12V source.

When the Zener is connected (green trace high) the voltage drops to 5.3V, from the Zener clamp.
(The voltage is slightly below the 5.6v nominal Zener voltage due to the low 10μA voltage through the Zener, which is well below is nominal rated test current).

 

The Zener is great, but it kind of defeats the purpose of a variable output regulator if the voltage can't be set above the Zener voltage.