I use Tor through Tails, which I am running from a DVD.
It works fine with the hard drive in place, and works fine with the hard drive removed but a USB memory stick in one of the other USB ports, but it crashes when booting up if there is no writeable drive connected. Clearly it needs to write something, which I guess explains why it has to delete when I close down.
Is it possible to work around this? It seems obvious that if there is no writeable media at all, there is no risk.
Update.... have tried it with the latest version of Tails. Does not work. Perhaps something to do with the hardware? It works fine from a USB. Its a mystery.
Of course it is on-topic! And it is reproducable by anyone who has the same equipment. Sorry but using a VM doesnt cut it.
Finding what the problem is might reveale a security issue, who knows.
Lenovo x61 with USB DVD player without hard drive; TAILS downloaded and installed via tails.boum.org following their instructions. I have submitted a bug report.