Is it possible to send a text as my un-rooted device is shutting down using Tasker or any other method?
You should use State &gt; Battery Level as a profile context with minimum and maximum battery as 3%. 

In the task, You can use %SMSRN to get phone number of last received SMS.

Then to check the condition of whether Last SMS text is received less than 10 minutes.

%TIMES has the current time in seconds. You need to use Variable Convert 
to get %SMSRT time in seconds and then do maths on the two values, 

You can also use the / and % maths operator to get things like 'remaining minutes'.