The practice of naming a designated survivor originated during the Cold War amid fears of a nuclear attack. Only Cabinet members who are eligible to succeed to the presidency (i.e., natural-born citizens over the age of 35) are chosen as designated survivors. For example, Secretary of State Madeleine Albright was not a natural-born citizen (having emigrated to the United States at age 9 from Czechoslovakia) and was thus skipped in the official line of presidential succession. The designated survivor is provided presidential-level security and transport for the duration of the event. An aide carries a nuclear football with them. However, they are not given a briefing on what to do in the event that the other successors to the presidency are killed.
So, to answer your question, I imagine that anyone after the Sec. of Labor is open to be the 'designated survivor' There was one time when Hillary was Secretary of State where she was also out of the country in London at a conference. They had a DS for that event as well, but if something happened, Clinton would have gotten the nod over the DS because her position was higher up the line of succession.
One of the things that happened in 2010's election was that EX-Speaker Pelosi no longer qualified for the luxury of USAF chauffeuring between SanFran and DC as well as Secret Service protection. So, from those stories, I think that the Speakership and President Pro-Tempore of the Senate both get these privileges as Numbers 2 & 3 in the succession. Boy, to have been a fly on the wall in that last trip back to DC in January 2011!
Obviously neither of these 2 positions qualifies as "Designated Survivor" as they attend the State of the Union address along with the V.President. Ah, no more Joe, nodding his head so enthusiastically at every Obama pause!