If you have Magic Sysrq enabled, you can do Magic Sysrq-t, which may give you some idea of what the system is doing, since you’ll get stack traces. As long as the kernel can talk to the keyboard, it should be able to get that.

en.wikipedia.org/wiki/Magic_sysrq

You maybe can’t see anything on your monitor, but if the system is working enough to generate the stack traces and log them to the syslog on disk (like, your kernel filesystem and disk systems are still functional), you’ll be able to view them on reboot.

If it can’t even do that, you might be able to set up a serial console and then, using another system running screen or minicom or something like that linked up to the serial port, issue Magic Sysrq to that and view it on that machine.

Some systems have hardware watchdogs, where if a process can’t constantly ping the thing, the system will reboot. That doesn’t solve your problem, but it may mitigate it if you just want it to reboot if things wedge up. The watchdog package in Debian has some software to make use of this.