The most common and most likely answer to this crossword clue is the 8 letter word STARCHED
I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "Made rigid" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case made rigid = starched.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 STARCHED mean?
STARCHED verb- To apply or treat with laundry starch, to create a hard, smooth surface.
- Of a garment: having had starch applied.
- Stiff, formal, rigid; prim and proper.