The most common and most likely answer to this crossword clue is the 11 letter word ESCHEATMENT
I've seen this crossword clue in The Times
E
S
C
H
E
A
T
M
E
N
T
More clues leading to the result ESCHEATMENT
Buddy explains!
The straight part
We know that "Procedure with unclaimed property" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case procedure with unclaimed property = escheatment.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.