How do you preserve rotting paper?

Some papers are not designed to last for a long period of time and will either be eaten away by their own acid content, or react with water vapour in the air, or will dry out and simply crumble away. There is very little that can be done to prevent any of these processes, beyond sealing the paper inside plastic sheets (a process called laminating) to prevent air or moisture getting to it.

Depending on what is on the paper you might consider scanning the text or image onto fresh paper, or photographing it and preserving the content in that way.

It is a feature of modern "throw-away" lifestyles that most of the written and printed paper material we use today will not last 100 years, compared with the books and documents of the early medieval period that were written on parchment and have lasted up to 1200 years - and can easily last another 1000.