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Proxmox host stops responding, LXC continues
(infosec.pub)
Proxmox VE is a complete, open-source server management platform for enterprise virtualization. It tightly integrates the KVM hypervisor and Linux Containers (LXC), software-defined storage and networking functionality, on a single platform. With the integrated web-based user interface you can manage VMs and containers, high availability for clusters, or the integrated disaster recovery tools with ease.
I'm running it on both the host and the container
There you go :) I’ve had a Pi running Tailscale and it ws not reachable using its local IP (it was accessible when using Tailscale IP) when Tailscale was started. When I was using Tailscale for site-to-site connectivity (subnet router) I ran it in an LXC container on PVE, so I’d advise you try that. Avoiding installation of additional software on the hypervisor seems like a smart idea - whenever I can I put stuff in containers/VMs.