[Nexus 6  Original Android Development] :
Trying to run busybox by itself gives you:

root@shamu:/system/xbin # busybox
BusyBox v1.23.2-Stericson (2015-04-10 10:51:32 CDT) multi-call binary.
BusyBox is copyrighted by many authors between 1998-2012.
Licensed under GPLv2. See source distribution for detailed
copyright notices.

Usage: busybox [function [arguments]...]
or: busybox --list[-full]
or: busybox --install [-s] [DIR]
or: function [arguments]...

BusyBox is a multi-call binary that combines many common Unix
utilities into a single executable. Most people will create a
link to busybox for each function they wish to use and BusyBox
will act like whatever it was invoked as.

Currently defined functions:
[, [[, acpid, adjtimex, arp, arping, ash, awk, base64, basename, beep,
blkid, blockdev, brctl, bunzip2, bzcat, bzip2, cal, cat, catv, chat,
chattr, chgrp, chmod, chown, chroot, chrt, chvt, cksum, clear, cmp,
comm, conspy, cp, cpio, crond, crontab, cttyhack, cut, date, dc, dd,
deallocvt, depmod, devmem, df, diff, dirname, dmesg, dnsd,
dnsdomainname, du, dumpkmap, echo, ed, egrep, eject, env, ether-wake,
expand, expr, fakeidentd, false, fatattr, fbset, fbsplash, fdflush,
fdformat, fdisk, fgconsole, fgrep, find, findfs, flock, fold, free,
freeramdisk, fsck, fsck.minix, fstrim, fsync, ftpd, ftpget, ftpput,
fuser, getopt, grep, groups, gunzip, gzip, hd, hdparm, head, hexdump,
hostid, hostname, httpd, hush, hwclock, id, ifconfig, ifdown,
ifenslave, ifplugd, ifup, inetd, insmod, install, ionice, iostat, ip,
ipaddr, ipcalc, ipcrm, ipcs, iplink, iproute, iprule, iptunnel,
kbd_mode, kill, killall, killall5, klogd, last, less, linux32, linux64,
ln, loadfont, loadkmap, logger, logname, logread, losetup, ls, lsattr,
lsmod, lsof, lspci, lsusb, lzcat, lzma, lzop, lzopcat, makedevs,
makemime, man, md5sum, mdev, microcom, mkdir, mkdosfs, mke2fs, mkfifo,
mkfs.ext2, mkfs.minix, mkfs.vfat, mknod, mkswap, mktemp, modinfo,
modprobe, more, mount, mountpoint, mpstat, mt, mv, nameif, nanddump,
nandwrite, nbd-client, nc, netstat, nice, nmeter, nohup, nslookup,
ntpd, od, openvt, patch, pgrep, pidof, ping, ping6, pipe_progress,
pivot_root, pkill, pmap, popmaildir, powertop, printenv, printf, ps,
pscan, pstree, pwd, pwdx, raidautorun, rdate, rdev, readahead,
readlink, readprofile, realpath, reformime, renice, reset, resize, rev,
rm, rmdir, rmmod, route, rpm, rpm2cpio, rtcwake, run-parts, runlevel,
rx, script, scriptreplay, sed, sendmail, seq, setarch, setconsole,
setfont, setkeycodes, setlogcons, setserial, setsid, sha1sum,
sha256sum, sha3sum, sha512sum, showkey, shuf, slattach, sleep, smemcap,
sort, split, start-stop-daemon, stat, strings, stty, sum, swapoff,
swapon, switch_root, sync, sysctl, syslogd, tac, tail, tar, tcpsvd,
tee, telnet, telnetd, test, tftp, tftpd, time, timeout, top, touch, tr,
traceroute, traceroute6, true, tty, ttysize, tunctl, ubiattach,
ubidetach, ubimkvol, ubirmvol, ubirsvol, ubiupdatevol, udhcpc, udhcpc6,
udpsvd, umount, uname, unexpand, uniq, unlink, unlzma, unlzop, unxz,
unzip, uptime, users, usleep, uudecode, uuencode, vconfig, vi, volname,
wall, watch, watchdog, wc, wget, which, who, whoami, whois, xargs, xz,
xzcat, yes, zcat, zcip

root@shamu:/system/xbin #

What this means is that anything that calls any of those commands listed in the first section code section would work as long as busybox is in /system/xbin as that's where they're linked to. IF you delete/rename/whatever that busybox binary, none of those commands would work. For something to work on the busybox included in UKM, it needs to be explicitly called by the full path. This is the reason that UKM sets a $BB variable to it's busybox, then calls all of it's commands as '$bb cat' for instance. This avoids the command being called as just 'cat' which would look in /system/bin or /system/sbin or /system/xbin for a 'cat' file to execute. Which depending on the busbybox version might give different results than expected.

Now, that being said. I tried removing my busybox binary and basic commands still worked.

This is because if you look at /system/bin :

root@shamu:/system/bin # ls -l | grep toybox
lrwxrwxrwx root root 2015-10-23 12:45 acpi -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 basename -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 blockdev -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 bzcat -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cal -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cat -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 chcon -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 chgrp -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 chmod -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 chown -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 chroot -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cksum -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 clear -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cmp -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 comm -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cp -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cpio -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 cut -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 date -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 dirname -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 dmesg -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 dos2unix -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 echo -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 env -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 expand -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 expr -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 fallocate -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 false -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 find -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 free -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 getenforce -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 getprop -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 groups -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 head -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 hostname -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 hwclock -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 id -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 ifconfig -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 inotifyd -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 insmod -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 kill -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 ln -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 load_policy -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 logname -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 losetup -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 lsmod -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 lsusb -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 md5sum -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 mkdir -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 mknod -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 mkswap -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 mktemp -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 modinfo -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 more -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 mountpoint -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 mv -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 netstat -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 nice -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 nl -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 nohup -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 od -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 paste -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 patch -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 pgrep -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 pidof -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 pkill -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 pmap -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 printenv -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 printf -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 pwd -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 readlink -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 realpath -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 restorecon -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 rm -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 rmdir -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 rmmod -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 route -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 runcon -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 sed -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 seq -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 setenforce -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 setprop -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 setsid -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 sha1sum -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 sleep -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 sort -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 split -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 stat -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 strings -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 swapoff -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 swapon -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 sync -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 sysctl -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 tac -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 tail -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 tar -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 taskset -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 tee -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 time -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 timeout -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 touch -> toybox
-rwxr-xr-x root shell 254284 2008-08-01 08:00 toybox
lrwxrwxrwx root root 2015-10-23 12:45 tr -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 true -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 truncate -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 umount -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 uname -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 uniq -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 unix2dos -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 usleep -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 vmstat -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 wc -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 which -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 whoami -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 xargs -> toybox
lrwxrwxrwx root root 2015-10-23 12:45 yes -> toybox

Oh, we have all the same symlinks there, but pointing to 'toybox'.... I wonder if this might be a failsafe busybox install?

root@shamu:/system/bin # toybox
acpi base64 basename blkid blockdev bzcat cal cat chattr chcon chgrp
chmod chown chroot cksum clear cmp comm cp cpio cut date dd df dirname
dmesg dos2unix du echo egrep env expand expr fallocate false fgrep
find free freeramdisk fsfreeze getenforce getprop grep groups head
help hostname hwclock id ifconfig inotifyd insmod install kill killall
ln load_policy logname losetup ls lsattr lsmod lsusb makedevs md5sum
mkdir mkfifo mknod mkswap mktemp modinfo more mount mountpoint mv
nbd-client nc netcat netstat nice nl nohup od partprobe paste patch
pgrep pidof pivot_root pkill pmap printenv printf pwd pwdx readlink
realpath renice restorecon rev rfkill rm rmdir rmmod route runcon
sed seq setenforce setprop setsid sha1sum sleep sort split stat strings
swapoff swapon switch_root sync sysctl tac tail tar taskset tee time
timeout top touch tr traceroute traceroute6 true truncate tty umount
uname uniq unix2dos usleep vconfig vmstat wc which whoami xargs yes

Well, it's not a full featured busybox... but it retains your basic commands so that you don't lose basic functionality when you're upgrading/changing/don't have busybox.

Hopefully that helps explain it a little bit.

Basically, unless the application is using the functions present in busybox but not in toybox... You'd never notice the difference by deleting all of your busybox binaries. However, you're still not using the one installed by UKM. It's literally impossible for that happen unless you redirect every one of those symlinks to it's path, or explicitly call it by full path.