Flimsy, easily broken (7)
I believe the answer is:
fragile
I believe this clue is a double definition.
'flimsy' is the first definition.
(I know that flimsy can be written as fragile)
'easily broken' is the second definition.
(I've seen this before)
(Other definitions for fragile that I've seen before include "Delicate, tenuous" , "Delicate; easily broken" , "Brittle" , "Liable to break easily" , "Easily-damaged" .)