The purpose of the hardware is to hold the vertebrae still while bony fusion occurs (internal fixation). Broken rods occur because bony fusion fails to occur, allowing continuous motion between two vertebrae. Eventually the metal rods suffer from metal fatigue and fracture. This happened to me at two levels and I had to have a huge revision to fix it.
I do not think a flexible rod would achieve the purpose of holding the vertebrae still over a period of months (internal fixation) while bony fusion occurs. Bony fusion by definition means joining two or more vertebrae together into one bone. We all know that a solid bone is not flexible or bendable. So I do not see how the biomechanics of fusion can possibly go together with flexibility.
It seems like you are hoping for some version of dynamic stabilization, as Linda suggests. There is some info about this on Pubmed.
Good luck in your search. I will be curious to hear what you find out.
Gayle, age 48
Oct 2010 fusion T8-sacrum w/ pelvic fixation, TLIF at L4/5.
Feb 2012 major lumbar revision for broken rods @ L2-3-4
Aug 2015 rods broken L5, A/P revision 9/23
mom of Leah, 13 y/o, diagnosed '08 with 26* T JIS (age 6)
4/08 26 degrees, brace 16 hrs/day
9/08 17 deg. OOB - brace discontinued
9/09 30 deg, resuming brace
5/10 VBS Dr Luhmann Shriners St Louis
4/15 stable 5 yrs post-op, 18* T/ 22* L, Risser 2
also mom of Torrey, 10 y/o son, 16* T, stable