Frequently you can buy a ticket but there are no seats showing available on the map. Some are held back for airport check-in and sometimes they are overbooked.
YOu cannot tell by the on line seat map if the flight is oversold.
THe airline "holds back" many seats for assignment at the airport for such purposes as giving last minute frequent flyers a better selection.
If a lot of people book but don't bother to select seats, the flight can become oversold while seats are still showing available on the seat map.
On some but not all airlines, being able to select a seat lowers your chances of being bumped.
But the OP asked the opposite question, can a flight be oversold if there are seats available for assignment. The answer is no, airlines don't assign more then one passenger to a seat.
While it is true the airline will not assign more than one person to a seat it is very possible for a flight to be oversold when there are seats still available on a seat map.
The airline doesn't force you to select a seat in advance (especially those airlines that charge for seats) so if enough people wait to select a seat the plane could most certainly be oversold with seats still open for assignment.
But the OP asked the opposite question, can a flight be oversold if there are seats available for assignment. The answer is no, airlines don't assign more then one passenger to a seat. .....................
Not so. A couple of years ago I was on Delta settled in my assigned seat when a fellow showed up and requested I remove myself from his seat. I called the FA and showed her my printout and he showed her his print out. Both were for my seat. FA told the other fellow, "sorry, but he was in the seat first". Only time that ever happened to me. Not sure what happened to the other fellow as I returned to my book.