The most common and most likely answer to this crossword clue is the 10 letter word CHROMOSOME
I've seen this crossword clue in The Guardian
C
H
R
O
M
O
S
O
M
E
More clues leading to the result CHROMOSOME
Buddy explains!

The straight part
We know that "Handed down item" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case handed down item = chromosome.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 CHROMOSOME mean?
CHROMOSOME noun- A linear arrangement of condensed DNA and associated proteins (such as chaperone proteins) which contains the genetic material (genome) of an organism.