Some games in the classical collections are not finished!

It's simply how these games, historically, have been recorded, and they DO stop at that point.

It happens very often that masters and grandmasters do not play the game until checkmate. The player who is obviously losing simply decides to resign.

This decision saves him both the pain and the energy to go to the end of the game, so he can start concentrating on the next game instead. It is also seen as a kind of courtesy to his opponent: if you continue playing a lost position it can be interpreted somehow like you are only waiting for your opponent to make a mistake because it is the only way you could not lose.

It can also happen that both players agree that the game is going to be a draw, because with a lot of experience you can recognize such cases. So they both agree to stop the game by offering each other a draw, which is permitted by the rules of chess. If the referee also agrees, the game is stopped and recorded as a draw.

There can also be other special cases:
  • A player can forfeit at some point in the game if he feels that, for any reason, he cannot continue (maybe he has caught a cold and must take some rest)
  • A player can behave badly in the tournament room and the referee decides to declare his opponent as the winner and to exclude him from the competition
  • ...

If you want to know why the game has been stopped, just tap
Game > Game information
Look at the result. If it's 1-0 or 0-1, then one player resigned. if it's 1/2-1/2, it was a draw by mutual agreement.

There is also a special case which happens very seldom. The result "*" (a star) means that the game has been unfinished. Maybe the tournament has been interrupted, or it is an historical game which has not been fully retrieved, and we do not know how it has ended.