Girl’s relative almost died alone (10)
I believe the answer is:
unassisted
'alone' is the definition.
(thesaurus)
'girl's relative almost' is the wordplay.
'girl's' becomes 'unas' (girl's name).
'relative almost' becomes 'sisted' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'unas'+'sisted'='UNASSISTED'
'died' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.
(Other definitions for unassisted that I've seen before include "Solo" , "Getting no help" , "Without help" .)