So some of services allow you to get email or push notifications. Thing is that probably you already receiving like a ton notifications per minute, and it really easy to miss important one.
There kind of was email from smoke detector that house if on fire, but it got lost somewhere between Twitter alerts and Instagram likes.
So for really-really important you can configure:
- email → call in Itfff.com (if you fortunate to live in US)
- email → Twilio.com in Zapier.com (if you even more fortunate to live in other place). Twilio.com will allow you to call yourself for free. Zapier.com will allow to make 100 email → call transactions in month. Should be enough (its more "routine" than "important" if theres more than 100)
Don't forget to put loud and distinctive ringtone to notification number, and allow it to pass "Do Not Disturb" mode.