STORY UPDATED: check for updates below.

Dangerous

Can you change your voicemail on your landline or cellphone when the phone has no service, data or connection to Wi-Fi? No, that's not true: Both T-Mobile and AT&T said that that was not possible.

The claim appeared in a Facebook post (archived here) on April 14, 2020. It opens:

EMERGENCY TIP!!!! If you ever find yourself in a dire situation and your phone is about to die or you have no service CHANGE YOUR VOICEMAIL!!! You don't need data or service to do so. Change it and state the time and your location!!! Please spread this around!!

This is what the post looked like on Facebook on April 29, 2021:

(Source: Facebook screenshot taken on Thu Apr 29 13:32:28 2021 UTC)

Lead Stories asked the Cellular Telecommunications Industry Association if this was a safe thing to do in an emergency. A spokesperson emailed on September 14, 2021, "Wireless consumers may be able to access their voicemail box from a landline when necessary, and they should contact their provider for more information ... Please see more information, including how to preserve a device's battery life, under 'During an emergency or a disaster' here: https://www.ctia.org/consumer-resources/emergency-preparedness"

AT&T emailed us on September 17, 2021, that:

When not on a cellular voice or data connection, customers can access and change their voicemail greetings using Wi-Fi calling from their device, or from another phone with service - including a landline phone.

A Verizon spokesperson emailed on September 17, 2021:

While you could dial *86 or change your voicemail greeting with visual voicemail if your battery was dying...you would still need cell service or a data connection of some sort (like wi-fi) in order to allow that new greeting to update on our servers.

If you do get caught in a situation where you're running low on battery, the Alpine Rescue Team in Evergreen, Colorado, recommended these steps in an October 23, 2021 Facebook post:

1. Call 911 for help. Don't waste your time calling a friend or changing your voicemail message.
2. If you're afraid you don't have enough power for a call or if you have too little signal, text 911 for help. Most 911 centers can receive a text. It takes much less signal to get a text through than a voice call and uses less battery power. Also, your phone automatically retries sending the message if it doesn't go through immediately.
3. Stay put. Moving makes it harder for authorities to track you down. They'll know your approximate location from the data received by the cell tower.
4. Maximize your battery life. Turn off everything you don't need including apps, Wi-Fi and Bluetooth. Also, keep your phone warm. If it's cold, there's a bigger drain on the battery.