If you look at it through a time scale, digital archiving is relatively new. There is no specific format favored either. Is some kind of bitmap WYSIWYG the perfect storage, or do we OCR? The technology evolves so rapidly that as soon as you've made a choice, ordered it, had it built up, set up and trained personnel on its use, the system has been made obsolete.
But as Neko points, something has to be done now. On the other side, we should trust the conservators entrusted with this repository. Every library has contingency plans.
No one today dealing with books is totally computer illiterate, libraries use digital indexes and subscriptions. A digitizing plan is usually not far in the works.
Something similar happened in Montréal about 10 years ago. Fire broke out in an important historical library. It was quickly put out but the water sprayed by the sprinklers leaked down to the basement's more priceless documents. The most important damage was noticed much later as the paper started to rot and decay. An alarm was sounded by the curators much too late, the damage was irreparable. Companies specailized in recovery of civil property were hired, but they lacked the technical expertise necessary for ancient artefacts and submitted the documents to more harm. There was a popular movement set up and some duplicate documents were donated to the library. An amazing number of works were retrieved this way and others the library did not have, but manuscripts, the more precious, were totally lost, and the ones that can be restored will not for a long time due to a lack of funds. Now what's left is in a brand new library that was built with the aid of emergency governmental funds.
There was a beautiful documentary on PBS this week about the library of Herculanum destroyed in 79AD by the erruption of mount Vesuvius. The reason for my mentionning this is for the digital technology shown throughout the program, meant to decrypt totally unreadable charred texts. It was possible through distribution of digital reproductions, like Steve pointed out, for scholars across the world to study the documents without traveling to physically study them. In this light, some restoration of the most precious documents, in the fire that we've just witnessed, will be possible .
Luckily this fire was not as bad as the one that destroyed the Library of Alexandria...
