Yes, it is possible. If it is difficult depends on the work others have done. IF it is code and follows the "Clean Code" principles aswell as using standard frameworks then it should easy to take over the code.
If the previous programmers did not respect general coding conventions or use exotic frameworks, it might become difficult.
Personally I would never do a "fresh start" before investigating the codebase. Some programmers prefer "fresh starts" only because they are used to other frameworks or different styles (or languages).
If have worked on development projects for years (I mean, one project going on for years). The project team changed much since I joined. I was not the first one on the project and not the last one. Still it was possible to take over the project.
After all when a codebase grows it becomes more difficult and difficult to get into. But the risk to develop it newly is not to underestimate. Nobody can guarantee you it becomes actually better.
therefore I would look at the old code:
- did the previous developers use standard frameworks (for example Zend Framework, jQuery, Wicket etc)
- did the previous developers use tools to verify standard quality (code style tools like Checkstyle, or other tools like Findbugs)
- did the previous devs create Unittests (phpunit, Junit etc) and how much do the test cover the code (40% is not acceptable, >85% is very good)
- is the code documented (Java/PHPDoc, additional documents
Then look at the new devs.
- have they experience with the same tools, languages etc?
- do they follow clean code standards?
- are they willing to write docs?
Ask them, why exactly they want a fresh start. There is a learning curve when adapting old software, but this cannot be the exact reaons. It must be something like circular dependencies, multithreading issues, exotic and not maintainable frameworks etc.
Only if I knew this I would decide if it is better to start over again. Remember, it is your money and they need to tell you why you should pay for the same work twice.