It is not currently possible to save the code for the callback function inside of the ".fig" file or have the figure add the callback function to the path, however there is a possible workaround.
Instead of saving the figure directly as a ".fig" file, you can instead save a function or script which can generate this file. Note that this script can the original program which made the figure, or a new file to simply load the necessary data in order to recreate the figure. Once this script or function exists, you can then define the desired callback function as a local function within your file. This way, whenever you want to view the figure, you will also have access to the appropriate callback function.
Note: The ability to define local functions within a script was introduced in the R2016b release of MATLAB.
