The most common and most likely answer to this crossword clue is the 5 letter word HOGAN
H
O
G
A
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More clues leading to the result HOGAN
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The straight part
We know that "earthen abode" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case earthen abode = hogan.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 HOGAN mean?
HOGAN noun- A one-room Navajo dwelling or ceremonial lodge, constructed of wood and earth and covered with mud.