Our house is 40 years old with the original bathroom sink... There is an overflow hole on the top inside of the sink, which is still open with water in it and smells... Some one closed off with metal on the overflow drain in the pipe you can see where the holes were... We unblocked one on the surface but cannot get high enough to open it up... Why would they want to close this off (The original owners at the time)

Some people like to close overflow holes to be able to fill sink higher than with overflow hole open. But I would recommend that you open it and leave it open. Overflow hole is a good safety device and can prevent lots of damage caused by overflowing sink.