Property close to collapse, say (6)
I believe the answer is:
estate
'property' is the definition.
(estate is a kind of property)
'close to collapse say' is the wordplay.
'close to' says to take the final letters (the close/ending of).
'say' becomes 'state' (synonyms).
The final letter of 'collapse' is 'e'.
'e'+'state'='ESTATE'
(Other definitions for estate that I've seen before include "Property and possessions of the deceased" , "park perhaps" , "The entire property of a deceased person" , "Follow on" , "Tea-set (anag.)" .)