The most common and most likely answer to this crossword clue is the 7 letter word CRAWLED
C
R
A
W
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D
Buddy explains!

The straight part
We know that "behaved abjectly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case behaved abjectly = crawled.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 CRAWLED mean?
CRAWLED verb- To creep; to move slowly on hands and knees, or by dragging the body along the ground.
- To move forward slowly, with frequent stops.
- To act in a servile manner.
- (with "with") See crawl with.
- To feel a swarming sensation.
- To swim using the crawl stroke.
- To move over an area on hands and knees.
- To visit while becoming inebriated.
- To visit files or web sites in order to index them for searching.