My advice: 1. Suggest that the work to replace it is prioritized commensurate with the business impact caused whilst re-establishing service as if it went down right now 2. Remind them that it will go down at the worst possible time. 3. Ensure your name is attached to these two warnings. 4. Promise yourself you wouldn't run your business this way. 5. Get on with your life.
- Make a plan of exploratory steps that could trigger a failure, in order of increasing risks.
- Then, if necessary, get a formal sign-off from someone with authority (perhaps a director of the company) to proceed with each step.
Steps like that, which are usually very low risk but do risk taking down an unknown service, might include things like (just ideas from other comments):
- Logging in to the server at all.
- Splicing something into the network switch.
- Cloning filesystems or disk images.
- Cloning the process memory or system memory.
- Cloning the image or other things if it's in a VM.
- Running strace gdb, or packet tracing.
- Swapping the power source live.
These days, it is often possible to transfer a full working system into a VM on a more modern, powerful machine, and after doing that, it's a great relief to everyone because it's no longer hardware dependent.
I've done that with some legacy systems that were originally on bare metal, and are now still running nearly 20 years later in reliable VMs, with no change to the running software. Usually running faster and with more memory doesn't break a working system.
But doing it on a service that can't be taken down even for a moment is quite an interesting adventure! :-) It is possible, but technically challenging, as long as you can obtain disk and memory images from the live system and then capture changes fast enough to perform a hot transfer.