This is a bit of a misunderstanding of how SMTP works.

If you run and maintain your own SMTP server and it goes down, you won't be able to send email.

Everyone else will still be able to send email to you, and it will be delivered to you, and you'll be able to read it.

Now, if you break Postfix or something on your server and start bouncing emails then you can be in trouble, or if you mess up the DNS somehow.

But generally running your own mail server is a set it up and leave it alone type of affair. Any junior level hacker can cobble one together with guides online and have it up and running with no problems in a few hours.