The most common and most likely answer to this crossword clue is the 8 letter word THATCHED
I've seen this crossword clue in The Daily Telegraph
T
H
A
T
C
H
E
D
More clues leading to the result THATCHED
Buddy explains!

The straight part
We know that "covered in straw" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case covered in straw = thatched.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does THATCHED mean?
THATCHED verb- To cover the roof with straw, reed, leaves, etc.