Tom brought up some good points. I myself, when I was still freelancing had many clients who came to me precisely because of previous developer nightmares, especially hired through elance/odesk networks.

However, there are also other cases. Relationship/communication is very important, and so is price. Both might trigger wanting to switch developers.

To answer your question, you should make sure to have a list of external/3rd party frameworks used, how well-commented the code is and obviously access to the full source code.
Any respectable company will assess the source code before suggesting a re-code or estimating the time/cost load.

Feel free to reach out if you need help with your specific code.