Will an incoming text trigger Storage space running out Some system functions may not work ?

I want to know if the above notification will be triggered by an incoming text message? Or what other events can trigger it?

I need to know if a text was sent to me that triggered this notification. I have read that even if you clear some memory, the text will be lost and not be received. Thanks

It is possible that a new text message would require that the data file be made bigger to store the new message.
If the attempt to make it bigger fails, it is reasonable to assume that you would get this notification.

Given the nature of how the SMS system works, I would expect the message to be lost if the write to the data file fails.