One approach could be to use PID namespaces:
Boot your system with a init=/some/cmd as kernel parameter, where /some/cmd forks a process in a new namespace (CLONE_NEWPID) and runs /sbin/init in it (it will have PID 1 in that new namespace and pid 2 in the root namespace), then in the parent, execute your "program".
You'll probably want a way to control your program in one way or another (TCP or ABSTRACT Unix socket for instance).
You'll probably want to mlock your program in memory and close most references to the filesystem so that it doesn't rely on anything.
That process won't be seen from the rest of the system. The rest of the system will in effect run like in a container.
If that process dies, the kernel will panic which gives you an extra guarantee.
An inconvenient side-effect though is that we won't see the kernel threads in the output of ps.
As a proof of concept (using this trick to boot a copy of your system in a qemu virtual machine):
Create a /tmp/init like:
#! /bin/sh -
echo Starting
/usr/local/bin/unshare -fmp -- sh -c '
umount /proc
mount -nt proc p /proc
exec bash <&2' &
ifconfig lo 127.1/8
exec socat tcp-listen:1234,fork,reuseaddr system:"ps -efH; echo still running"
(you need unshare from a recent version of util-linux (2.14)). Above we're using socat as the "program" which just answers on TCP connections on port 1234 with the output of ps -efH.
Then boot your VM as:
kvm -kernel /boot/vmlinuz-$(uname -r) -initrd /boot/initrd.img-$(uname -r) \
-m 1024 -fsdev local,id=r,path=/,security_model=none \
-device virtio-9p-pci,fsdev=r,mount_tag=r -nographic -append \
'root=r rootfstype=9p rootflags=trans=virtio console=ttyS0 init=/tmp/init rw'
Then, we see:
Begin: Running /scripts/init-bottom ... done.
Starting
[...]
root@(none):/# ps -efH
UID PID PPID C STIME TTY TIME CMD
root 1 0 0 14:24 ? 00:00:00 bash
root 4 1 0 14:24 ? 00:00:00 ps -efH
root@(none):/# telnet localhost 1234
Trying ::1...
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
UID PID PPID C STIME TTY TIME CMD
root 2 0 0 14:24 ? 00:00:00 [kthreadd]
root 3 2 0 14:24 ? 00:00:00 [ksoftirqd/0]
[...]
root 1 0 2 14:24 ? 00:00:00 socat tcp-listen:1234,fork,reuseaddr system:ps -efH; echo still running
root 204 1 0 14:24 ? 00:00:00 /usr/local/bin/unshare -fmp -- sh -c umount /proc mount -nt proc p /proc exec bash <&2
root 206 204 0 14:24 ? 00:00:00 bash
root 212 206 0 14:25 ? 00:00:00 telnet localhost 1234
root 213 1 0 14:25 ? 00:00:00 socat tcp-listen:1234,fork,reuseaddr system:ps -efH; echo still running
root 214 213 0 14:25 ? 00:00:00 socat tcp-listen:1234,fork,reuseaddr system:ps -efH; echo still running
root 215 214 0 14:25 ? 00:00:00 sh -c ps -efH; echo still running
root 216 215 0 14:25 ? 00:00:00 ps -efH
still running
Connection closed by foreign host.
root@(none):/# QEMU: Terminated