If you read the recent entry in the "Baghdad Burning" Blog by Riverbend, the Girl Blogger who used to be in Baghdad and left for Syria, the welcome in neighbouring countries is no longer there.
Iraqis have to either go through a exit / re-entry process, become illegal refugees or return to Iraq.
This return is the fate of those who have no status, no money and have, therefore, only one option - return to Iraq to face death.