Drop off family’s cleaner (6)
I believe the answer is:
napkin
'cleaner' is the definition.
(napkins are used to clean things)
'drop off family's' is the wordplay.
'drop off' becomes 'nap' (drop off can mean to sleep).
'family' becomes 'kin' (synonyms).
'nap'+'kin'='NAPKIN'
(Other definitions for napkin that I've seen before include "Cloth square worn while eating" , "Cloth square used to protect clothing while eating" , "piece of material giving consumer protection" , "Serviette; diaper" , "Cloth rectangle worn at mealtime" .)