This is as tight as I can currently squeeze it:

echo "/home/code/work"|\
perl -pe's|(/[^/]+)|$`$1 |g'
[download]

Update: My previous, longer solutions:

perl -pe's|(/[^/]+)|$`$1$"|g' ### $" - DUH!
perl -l40p057e'$_=$;.$_;$;="$_/"'
perl -ne'print$1,$"while m|($&/[^/]+)|'
perl -e'$_=<>;print$1,$"while m|($&/[^/]+)|'
perl -e'@_=<>=~m|(/[^/]+)|g;print@_[0..$_],$"for(0..$#_)'
[download]