I was facing this issue this morning. My system was on for several weeks, and today it was showing disc full warnings. On brief analysis, I found that /var/log/ folder has grown massively. So cleaned up system logs, and ran Bleachbit as root user. Now in the Disk usage analyzer tool, it was showing my system is having enough disc space, and even the system was working as normal. But I was not able to download anything as I was still getting disk full notification. On googling I came to know that, even though I deleted but still those files may be open in some processes. To find it out , I ran lsof -n | grep deleted
. In my case, Chrome was still referring to some of the deleted logs. A simple restart solved this issue.