Non-Systemd Based Linux Services
Solution 1:
Typically you either use a dedicated supervisor daemon/process that you ensure starts at boot and that in turn starts, monitors and restarts other processes/daemons.
Traditionally in Linux that is also "init", which comes in a number of flavours. AntiX provides you with two init system flavours: sysVinit and runit.
Both of them should offer you the ability to start daemons at boot and restart failed daemons.
Wikipedia provides a fairly comprehensive list of additional (non init as well as init) supervisors : https://en.wikipedia.org/wiki/Process_supervision