Is it safe to leave a slow cooker (Crock-Pot) on unattended (for example, while you're at work and no one is home)? Or is that a fire hazard?
That's exactly what they are designed for!
In general their electrical construction, and possible failure modes fully support being left on unattended
They should pose no more fire risk than any other electrical kitchen device being left on at the wall e.g. an automatic toaster or kettle
Some slow cookers have automatic fuses that blow if the pot runs dry, but most seem to keep going with no ill effect. There is no reason for a slow cooker to run dry unless you leave the lid off for over a day!
As long as the cooker is in good electrical shape and nothing is touching the outside of the unit, it shouldn't be a problem. We usually try recipes out on a weekend first so we know how long they'll take and that the food won't burn, but we often leave it running while we're at work for things we cook regularly.