bbinit is a minimal init system based on busybox. It is mostly developed and tested on Arch Linux and Alpine Linux but should be usable on other Linux distributions if you're willing to experiment. (I have had some success using it to boot OpenSuSE, Slackware, and VoidLinux.)
Please note that bbinit simply launches a bare minimum of processes used to configure the system at startup and attempts to stop everything cleanly at shutdown. It is NOT a "service manager"
To setup bbinit on an existing system, refer to the instructions in the ./INSTALL file.
For a more detailed explanation of bbinit, check out the files in the ./usr/share/doc/bbinit/ directory. The file named "FILES.txt" is a good place to start.