As long as the wood stove is installed properly and you're not getting the wood stove too hot and you have the fire in the wood stove under control then yes you can leave a wood stove unattended to allow it to heat your home.
I leave my wood stove unattended when I leave the house to go grocery shopping or run errands etc and I also leave the wood stove going to heat the house during the night as well.
Never had a problem with leaving the wood stove unattended but just don't build a big roaring fire that could get out of control in the wood stove.
Make sure you allow the fire to burn for at least 30 minutes before you leave so that you can be sure the fire in the wood stove is burning proper.
Turn the damper down a little bit so that the wood stove will burn a slow burn to keep the house warm while you're away.
A lot of natural gas, propane and oil furnaces are left on while people sleep and while they are away and nobody thinks twice about that but even those heat sources could blow up a house or catch a house on fire.
Just never leave an open fireplace unattended because it can throw sparks out into your home and catch the house on fire while asleep or while you're away from the home.
But a fire contained in an enclosed wood stove is perfectly safe.