I've rescued pretty messed up systems before. In one case, a service went haywire and created tens of millions of <1kb files, eating up all the available inodes in the filesystem. The volume was only ~45% full, but you couldn't make any new files. If that happened here, it's unlikely the ssh process could start correctly since it creates locks, logs, and pid files. Those are mostly in /run, so it might be okay, but it does make me a bit antsy.