Yes you can leave your slow cooker on even when the food is fully cooked.
Just turn the heat setting down on the slow cooker once the food has been fully cooked so it doesn't evaporate all the water out the slow cooker too fast.
Also keep an eye on the slow cooker and as the water level goes down in the slow cooker then add some more water to keep it from drying out.
I've left food in my slow cooker and left the slow cooker on for two days while I finished up the food I made in it.
As long as the food is kept hot it's safe to eat although you can refrigerate the food and the slow cooker if you want too and then reheat the food with the slow cooker although it will take awhile to heat back up.