I want to know if there is any software that allows multiple users to make changes in the same database, without the database being centralized. Every user would have a copy of the database and changes from one user would apply to all copies.
Either that or there are users that act as servers and the rest as clients. For example users which are somehow considered trustworthy or have a high uptime would be servers.
IPFS (e.g. OrbitDB) and Retroshare are cool implementations of this concept.
Any distributed database does this - if you consider the users being the nodes of the database in that case.
Look at distributed hash tables for a start.
This is what blockchains are for
Blockchains only work for very small databases though, right?
They can be as big as you want them to be