Database design is different from application design in this regard.
Very often, client rethinking changes the application completely, but changes little, if anything, in the fundamental underlying data model of the enterprise. The reason for this is that clients tend to think in terms of business processes, but not in terms of fundamental data. Business processing and data processing are tightly coupled. Data storage is less tightly coupled.
In the days of classical database design, designers learned how to exploit this pattern, by dividing their database design into (at least) two layers: logical design and physical design. There are any number of times that a change of business process requires a complete rewrite of the application, and a major rework of the database physical design, but requires few, if any, changes to the logical design.
If your database design didn't separate out the layers like this, it's hard to tell what gets affected and what doesn't. Start with your tables and columns. Ask yourself if any of the changes require removing any column from the table it's in, or require inventing new columns. If the answer is no, you're in luck. Next, look at the constraints placed on the database (things like PRIMARY KEY, FOREIGN KEY, UNIQUE and NOT NULL). These constraints might be tightened or loosened by the client's changes. If not, you're in luck. If you didn't declare any constraints in the database, and chose to do all your integrity protection in application code, you're probably out of luck.
You still have a fair amount of work to do in terms of changing the indexes on the tables, and the way the application works with the data. But you've salvaged part of the investment in the old system.
The application itself is much more vulnerable to client changes in process than the database. If your database design was completely driven by your application design, you may be out of luck.