Beset by trouble, one's bordering on careless almost (2,8)
I believe the answer is:
in extremis
'beset by trouble' is the definition.
'one's bordering on careless almost' is the wordplay.
'one' becomes 'i' (Roman numeral).
'bordering on' becomes 'next' (I am not sure about the 'on' bit.**).
'careless' becomes 'remiss' (I've seen this before).
'almost' means to remove the last letter (most of the word but not all of it).
'remiss' with its last letter taken away is 'remis'.
'i'+'next'+'remis'='IN EXTREMIS'
(Other definitions for in extremis that I've seen before include "dying" , "as last resort" , "at a desperate point" , "Facing death" , "feeling desperation" .)