The most common and most likely answer to this crossword clue is the 7 letter word SWAMPED
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More clues leading to the result SWAMPED
Buddy explains!

The straight part
We know that "stuck in Slough" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stuck in slough = swamped.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 SWAMPED mean?
SWAMPED verb- To drench or fill with water.
- To overwhelm; to make too busy, or overrun the capacity of.
- To plunge into difficulties and perils; to overwhelm; to ruin; to wreck.
- Very busy; having too much to do