A fundamental understanding of cell shaping with confined flexible filaments, including microtubules, actin filaments, and engineered nanotubes, has been limited by the complex interplay between the cell membrane and encapsulated filaments. Here, combining theoretical modeling and molecular dynamics simulations, we investigate the packing of an open or closed filament inside a vesicle. Depending on the relative stiffness and size of the filament to the vesicle as well as the osmotic pressure, the vesicle could evolve from an axisymmetric configuration to a general configuration with a maximum of three reflection planes, and the filament could bend in or out of plane or even coil up. A plethora of system morphologies are determined. Morphological phase diagrams predicting conditions of shape and symmetry transitions are established. Organization of actin filaments or bundles, microtubules, and nanotube rings inside vesicles, liposomes, or cells are discussed. Our results provide a theoretical basis to understand cell shaping and cellular stability and to help guide the development and design of artificial cells and biohybrid microrobots.