The most common and most likely answer to this crossword clue is the 8 letter word NON-SKID
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More clues leading to the result NON-SKID
Buddy explains!

The straight part
We know that "Kind of sole you shouldn’t find on a slipper?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kind of sole you shouldn’t find on a slipper? = non-skid.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 NON-SKID mean?
NON-SKID adjective- Having a surface designed to prevent or reduce skidding; not able to skid or be skidded upon.