The behaviour of these functions is affected by settings in php.ini.
Here's a short explanation of the configuration directives.
The unserialize callback function will called (with the undefined class' name as parameter), if the unserializer finds an undefined class which should be instanciated. A warning appears if the specified function is not defined, or if the function doesn't include/implement the missing class. So only set this entry, if you really want to implement such a callback-function.
See also unserialize().