A shelter the woman had (4)
I believe the answer is:
shed
I believe this is a double definition.
'a shelter' is the first definition.
(I've seen this before)
'woman had' is the second definition.
(she'd)
'the' is the link.
(Other definitions for shed that I've seen before include "Basic building" , "Discard; small building" , "Kind of hut - discard it" , "lost" , "Discard (something)" .)