Handled soft fabric (4)
I believe the answer is:
felt
This clue is a double definition.
'handled' is the first definition.
(feel can mean to handle)
'soft fabric' is the second definition.
(I've seen this before)
(Other definitions for felt that I've seen before include "suitable for a fedora" , "Cloth of pressed wool and fur" , "Handled - material" , "checked by hand" , "investigated in touching way" .)