Call to undefined function cache_get() in hostmaster /includes/module.inc

Hostmaster went down and all Drush commands fail with:

PHP Fatal error:  Uncaught Error: Call to undefined function cache_get() in /var/aegir/hostmaster-7.x-3.130/includes/module.inc:754
Stack trace:
#0 /var/aegir/hostmaster-7.x-3.130/includes/module.inc(954): module_implements('system_theme_in...')
#1 /var/aegir/hostmaster-7.x-3.130/modules/system/system.module(2511): module_invoke_all('system_theme_in...')
#2 /var/aegir/hostmaster-7.x-3.130/includes/theme.inc(798): _system_rebuild_theme_data()
#3 /var/aegir/hostmaster-7.x-3.130/includes/theme.maintenance.inc(57): list_themes()
#4 /var/aegir/hostmaster-7.x-3.130/includes/bootstrap.inc(2872): _drupal_maintenance_theme()
#5 /var/aegir/hostmaster-7.x-3.130/includes/errors.inc(179): drupal_maintenance_theme()
#6 /var/aegir/hostmaster-7.x-3.130/includes/bootstrap.inc(2609): _drupal_log_error(Array, true)
#7 [internal function]: _drupal_exception_handler(Object(ParseError))
#8 {main}
  thrown in /var/aegir/hostmaster-7.x-3.130/includes/module.inc on line 754

This is usually the result of hostmaster's settings.php getting corrupted, which would be caused by a Verify task dying before the file was fully written (so part of it's missing).

More generally, this is the problem described in Support: Post installation: Fatal error: Call to undefined function cache_get() .