The most common and most likely answer to this crossword clue is the 6 letter word TWERPS
I've seen this crossword clue in The Daily Telegraph
T
W
E
R
P
S
More clues leading to the result TWERPS
Buddy explains!

The straight part
We know that "Those who exhibit really painful stupidity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case those who exhibit really painful stupidity = twerps.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 TWERPS mean?
TWERPS noun- A fool, a twit.
- A small or puny person; one regarded as insignificant, contemptible.
- A person who can be bullied playfully, or easily teased. Sometimes used as a pet-name (often for a younger sibling).