Soft, one went on to say, being cushioned (6)
I believe the answer is:
padded
'being cushioned' is the definition.
('padded' can be a synonym of 'cushioned')
'soft one went on' is the wordplay.
'soft' becomes 'p' (musical abbreviation for 'piano', soft).
'one went on' becomes 'added' (I've seen this in another clue).
'p'+'added'='PADDED'
'to say' acts as a link.
(Other definitions for padded that I've seen before include "Kind of cell for violent prisoners" , "Covered with thick material" , "Covered with anything soft; stuffed" , "Kind of soft cell for violent prisoner" , "Stuffed with soft material" .)