Borge,
Thanks for your post. As I understand, you need a 4V, 400mA LDO. The biasing resistor for your shunt regulator will control the amount of current you draw from this LDO. Please take a look at TPS73601 as it is low drop out LDO and may serve your purpose well. Please let me know if you have any further questions.
Regards,
Kartik