In the nature of things, the amount of valuable material recovered is going to be very small.
Not necessarily so. A lot depends on the period and how you define valuable.
For books from the later period, which used printed material for the recycling, the chance of finding unique or new texts is likely small. There are fewer “lost” works from the age of print simply because there were more copies to start with. But this isn’t the case for manuscripts. Many medieval works, for example, survive in single copies. Finding a second copy, even if it is only a fragment, of a work with a single exemplar would be extraordinarily valuable. Furthermore, finding a previously unknown edition of a printed work, especially an incunabulum, would be valuable to bibliographers.
And what is valuable is subjective and changes with the audience and over time. For instance, books are commonly discarded because they have been written in. But such annotations and marginalia are highly prized by bibliographers and those studying how texts were received. What someone thought was useful only for pulp in the eighteenth century might be highly prized in the twenty-first. I know many scholars who have literally wept upon finding a text that some nineteenth-century bookbinder has trimmed in order to make it the same size as all the other books on the shelf, destroying the marginalia and often portions of the text itself.
What will be found, though, will be fragments of longer works. But even a line or two from an Old English poem, for example, would be a huge find.