The most common and most likely answer to this crossword clue is the 7 letter word PETRIFY
I've seen this crossword clue in The Guardian
P
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More clues leading to the result PETRIFY
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The straight part
We know that "Make rigid/Make rigid" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make rigid/make rigid = petrify.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 PETRIFY mean?
PETRIFY verb- To harden organic matter by permeating with water and depositing dissolved minerals.
- To produce rigidity akin to stone.
- To immobilize with fright.
- To become stone, or of a stony hardness, as organic matter by calcareous deposits.
- To become stony, callous, or obdurate.
- To make callous or obdurate; to stupefy; to paralyze; to transform; as by petrification.