Can a toilet just randomly overflow even after not being used for 12 hours?

We came home last night (Monday night) to a FLOOD in our basement caused by our toilet. We had used it on Sunday night, but I had been down in the basement on Monday morning before going to work and there was no water that I noticed (I didn't go into the bathroom, but I didn't hear the toilet running either).
What happened? Could it just have started overflowing after we went to work?
it's totally RUINED our basement.

The only way I can see this happening is if someone plugged it, then you had a leak from your fill valve or pressure assist. Are you sure the supply line is intact? Is your sewer prone to back up from the main after a downpour? Why didn't your floor drain handle the overflow? Is the toilet set over a floor drain? Not a plumber.

toilet

Unless you tell us where the water came from, we cannot diagnose the problem. But something could have broken and caused the flood, but it would not have "unbroken" itself before you came home.

Did you have heavy rains that day? THe sewer may have backed up. Many towns do not have separate storm drains and sewer drains (many towns are changing that to meet epa reqs). So, if there is a heavy downpour, depending on conditions, it can back up the sewer. It could be very diluted from the rainwater, and not smell much. They do make check valves to help prevent this from happening, but they have their own problems, too.