The most common and most likely answer to this crossword clue is the 6 letter word REMISS
I've seen this crossword clue in Financial Times
R
E
M
I
S
S
More clues leading to the result REMISS
- Careless soldiers don’t hit target
- Negligent fail again?
- Negligent on subject of young girl?
- To send almost empty supplies is negligent
- Negligent about girl
- Negligent first couple of reports by teacher
- Fail to attend again? That's careless
- Careless Whisper, heartily covered by Island rock band first
- Forgetful miser’s destitute
- Lax procedure missing fences
Buddy explains!

The straight part
We know that "negligent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case negligent = remiss.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 REMISS mean?
REMISS adjective- At fault; failing to fulfill responsibility, duty, or obligations.
- Not energetic or exact in duty or business; careless; tardy; slack; hence, lacking earnestness or activity; languid; slow.