How does navigation stack work without a static map?

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AMCL is a Localization algorithm, i.e. it requires a map in order to compute the most likely pose of the robot.

If you don't have a map of the environment, you need a SLAM (Simultaneous Localization and Mapping) algorithm to build it. This allows the robot to incrementally build the map as it explores the environment. This exploration can be driven by human controls (i.e. joystick), it can be done moving randomly or it can use exploration algorithms (frontier-based exploration is the simplest).

Theoretically, you can move to a goal position without a map, but this is not path planning as the robot will simply move in a straight line toward the goal, because with no map there are no obstacles. From a practical point of view I think that most system will not allow you to do that.

Here some resources on SLAM with ROS Navigation Stack

http://wiki.ros.org/robotican/Tutoria...

http://wiki.ros.org/navigation#Naviga...

You can look for papers on SLAM, autonomous exploration, frontier-based exploration