Easily destroyed dossier penetrated by tabloid (7)
I believe the answer is:
fragile
'easily destroyed' is the definition.
(something fragile can be broken easily)
'dossier penetrated by tabloid' is the wordplay.
'dossier' becomes 'file' (I've seen this in another clue).
'penetrated by' indicates putting letters inside (I've seen this in other clues).
'tabloid' becomes 'rag' (informal term for a tabloid newspaper).
'file' enclosing 'rag' is 'FRAGILE'.
(Other definitions for fragile that I've seen before include "Breakable" , "Delicate; easily broken" , "Delicate, tenuous" , "Easily broken or damaged" , "Weak" .)