Here is what I know
At Flight Options, they don't really like to look at furloughed guys, BUT, they do require you to give up your seniority. They want a letter from your CP or something like that stating that you have been taken off of the seniority list. At Net Jets, they require you to give up your seniority but I am not sure of the method there. At Flex Jet, they not only require you to resign, they also want a letter from your parents or initial caregivers that they will personally take you out of any will if you go back to the airline, ever. (The Flex Jet thing was made up, I have no idea about them)