Read a couple articles on movie archiving recently. I believe they are stored long-term in two ways. In digital form on magnetic tape (I believe LTO is still the preferred format). And on polyester film, separated into three B&W strips which represent cyan, magenta and yellow.
The LTOs have to be updated about every 5 to 10 years, because new LTO drives are backward compatible with only two generations of the tapes. And it is a fairly costly and time consuming process, because of the increasing amounts of data that have to be transferred.
Properly stored, the film elements have the longest shelf life, on the order of a century.