LT1308
Production
The LT1308 is a micropower, fixed frequency boost DC/DC converter that operates from an input voltage as low as 1V. Capable of delivering 5V at load current...
Datasheet
LT1308 on Analog.com
OK, I did some testing.
1. Connecting pin 3 to a 10k to Vin does not affect start up.
2. Connecting pin 3, also, to Vout does affect operation by lowering the output voltage. I am sure it is because the circuit is attempting to draw power through the 10k resistor. Though, it does not make sense to see a significant drop in the output.
2-followup. I can connect to 100k and no effect on output, however it does still shuts down below 1.0Vin.
I did try to connect pin 3 to 2V and then lower Vin below 1.0V. LT1308 shut itself down as if pin 3 was connected directly to Vin. Must be an internal UVLO on the Vin; spec does have a minimum input voltage of 0.92V (though I see the drop out around 0.98V).