How can you buy a ticket and not have an assigned seat?
It happens, particularly in cases like this. If you buy tickets online and try to select a seat, it says, "airport check-in only." Same if you buy directly from the airline.
This doesn't mean that every time it says "airport check-in only" you're going to get bumped. There are several other reasons you may not get a seat when you buy a ticket. For example, if you buy tickets close to travel time, sometimes they don't give advance seat assignments. Also, only about 40-50% of the seats are available for advance check-in. The others are saved for airport check-in. That's why you can sometimes change to an aisle or window seat at the airport when none of those seats was available in advance.
It's always safer to have a seat assignment, even if it's a middle seat, if possible. You can always try to change it at the airport. Going to the airport without a seat assignment for a flight that's oversold can result in bumping. I've even heard of two people being assigned to the same seat in cases of oversold flights. That's a tough one to resolve...