I was really surprised that modern smartphones are not able to ring an alarm while they are turned off.
My daily driver, Sony Ericsson ELM, rings an alarm each morning I need it, for the last ~9 years. Even when it's off, even if the battery is dead (once had a problem with a charger, couldn't even boot the phone, but it rang each morning for a week).
My iPhone? If it dies, it dies. Not even talking about Android.