Person feeding furnace possibly losing head (5)
I believe the answer is:
eater
'person feeding' is the definition.
(someone eating)
'furnace possibly losing head' is the wordplay.
'furnace possibly' becomes 'heater' (a furnace heats things).
'losing head' means to remove the first letter.
'heater' with its first letter removed is 'EATER'.
(Other definitions for eater that I've seen before include "type of fruit" , "Person taking course" , "Taker of food" , "Consumer of food" , "Fruit (but not a cooker)" .)