You simply need to add the /etc/rc.local file and get it to run your stuff like this:
Add the file /etc/rc.local and make it executable
touch /etc/rc.local
chmod a+x /etc/rc.local
Add code to run your code to /etc/rc.local
#!/bin/bash
cd /home/debian
bash -c './a.out &>> a.log' &
exit 0
Put your binary in /home/debian/ on the device. Then reboot and observe it running in the log /home/debian/a.log
Why does this work? Because even though the /etc/rc.local is not added to base the BBB the facility is still present. You just need to add the file and it'll work as with all Linux systems.
You can see this if, before adding it, you run systemctl status rc-local.service
root@beaglebone:~# systemctl status rc-local.service
Warning: The unit file, source configuration file or drop-ins of rc-local.service changed on disk. Run 'systemctl daemon-reload' to reload units.
* rc-local.service - /etc/rc.local Compatibility
Loaded: loaded (/lib/systemd/system/rc-local.service; static; vendor preset: enabled)
Drop-In: /lib/systemd/system/rc-local.service.d
--debian.conf
Active: inactive (dead)
Docs: man:systemd-rc-local-generator(8)
See Active: inactive (dead) because the file /etc/rc.local is missing