This depends on each platform.

PC platforms are installing patches by editing/replacing existing files and adding new ones if necessary.

On game consoles patch as a whole is mounted next to base game when game is launched, it's not replacing physically installed files. Patch usually for assets doesn't include whole files, but only changed bits with informations where those changes in original files happened. So when game will want to load texture that was patched, system will read data from both base game for original data and patch for changed data.