Why did MySQL suddenly stopped on my server?

Yes, you should look at system logs before come to a conclusion. But there is a 95% chance that this happened due to lack of memory. You’ll have to upgrade your droplet if that’s the case. And while you’re at it you can create a more optimized environment for WordPress using a LEMP setup.

Every droplet I have ever created with an install of Wordpress will eventually crash MySQL, unless I take certain steps.

Mostly, what happens is that Wordpress is barraged with bots trying to login or gain access to your Wordpress account.

A few steps will diminish these attacks to rarely if ever crash MySQL:

• Install the plugin Login-lockdown
• Change your Wordpress Login Page (you will need to Google for that, as there is several ways to go about it) basically you are moving your Wordpress login page from wp-login.php to something else (for example mypersonalogin.php)
• set up swap (as mentioned in previous answers
• use 6G firewall in your .htaccess https://perishablepress.com/6g/

Lastly, I created a script that will check on MySQL and Apache and restart them if needed:

https://github.com/sierracircle/services-checker

Those things will not completely stop all bots or attacks on your Wordpress site, but they will stop the mindless bots that are searching for basic/common installs of Wordpress, which will make MySQL crash.

For fun, once you install Login-Lockdown, wait for a bit and then view the logs (under settings in Wordpress) and you will see all of the attempts that have been made to access your site. You can see all of the common names and passwords that the bots use to try and login with.

What is your Droplet size? Are you using 512MB Droplet?

What comes to my mind is that if MySQL could got killed because it left without available RAM.

As of Ubuntu 16.04, default MySQL is 5.7, which requires at least 1GB of RAM on Droplet.

If you are really using 512MB Droplet I could recommend you upgrading to higher or setting-up swap