MySQL server has gone away upgrade error

As reported by Jeffery Watkins:

I am trying to upgrade a 1.9.10+ site to 2.0. I am getting this message:

Debug info: MySQL server has gone away
SELECT 'x' FROM mdl_files WHERE pathnamehash = ? LIMIT 0, 1
[array (
0 => 'fbf2ce18359e1764fc2a2b38db5ef9262cadd984',
)]
Stack trace:

• line 391 of /lib/dml/moodle_database.php: dml_read_exception thrown
• line 691 of /lib/dml/mysqli_native_moodle_database.php: call to moodle_database->query_end()
• line 1540 of /lib/dml/moodle_database.php: call to mysqli_native_moodle_database->get_recordset_sql()
• line 1525 of /lib/dml/moodle_database.php: call to moodle_database->record_exists_sql()
• line 1509 of /lib/dml/moodle_database.php: call to moodle_database->record_exists_select()
• line 142 of /lib/filestorage/file_storage.php: call to moodle_database->record_exists()
• line 130 of /lib/filestorage/file_storage.php: call to file_storage->file_exists_by_hash()
• line 333 of /lib/db/upgradelib.php: call to file_storage->file_exists()
• line 359 of /lib/db/upgradelib.php: call to upgrade_migrate_files_course()
• line 359 of /lib/db/upgradelib.php: call to upgrade_migrate_files_course()
• line 100 of /lib/db/upgradelib.php: call to upgrade_migrate_files_course()
• line 592 of /lib/db/upgrade.php: call to upgrade_migrate_files_courses()
• line 1309 of /lib/upgradelib.php: call to xmldb_main_upgrade()
• line 264 of /admin/index.php: call to upgrade_core()

Tried upgrading via the command line:

-->System
++ Increasing size of user idnumber field, this may take a while... ++
!!! Error reading from database !!!
!! MySQL server has gone away
SELECT 'x' FROM mdl_files WHERE contenthash = ? LIMIT 0, 1
[array (
0 => '54a8f1a3cb047c47beac209d11316c7cba6b921e',
)] !!
!! Stack trace: * line 391 of /lib/dml/moodle_database.php: dml_read_exception thrown

• line 718 of /lib/dml/mysqli_native_moodle_database.php: call to moodle_database->query_end()
• line 1553 of /lib/dml/moodle_database.php: call to mysqli_native_moodle_database->get_recordset_sql()
• line 1538 of /lib/dml/moodle_database.php: call to moodle_database->record_exists_sql()
• line 1522 of /lib/dml/moodle_database.php: call to moodle_database->record_exists_select()
• line 1173 of /lib/filestorage/file_storage.php: call to moodle_database->record_exists()
• line 791 of /lib/filestorage/file_storage.php: call to file_storage->deleted_file_cleanup()
• line 336 of /lib/db/upgradelib.php: call to file_storage->create_file_from_pathname()
• line 359 of /lib/db/upgradelib.php: call to upgrade_migrate_files_course()
• line 100 of /lib/db/upgradelib.php: call to upgrade_migrate_files_course()
• line 592 of /lib/db/upgrade.php: call to upgrade_migrate_files_courses()
• line 1309 of /lib/upgradelib.php: call to xmldb_main_upgrade()
• line 106 of /admin/cli/upgrade.php: call to upgrade_core()
  !!
  <br />
  <b>Fatal error</b>: Exception thrown without a stack frame in <b>Unknown</b> on line <b>0</b><br />