When designing a game, it is important to set rules as to what constitutes the end of a game, to set winners, losers, and also to stop the game from going on senselessly. This piece is how I see these parameters being set.
Although this is in a sense based on abstract games, this can be applied to board games in a general sense. Board games, after all, have a win and loss condition. These two conditions are mutual to each other by the simple fact that the inverse of one is the other, e.g. you win in Chess by checkmating your opponent and lose by being checkmated.
In some cases there are draw conditions, where no one wins or loses. To use chess again as an example, the draw conditions are stalemate, perpetual check and 50 moves without a capture or pawn move (don't argue, this is what FIDE says).
Games usually focus on either procuring a win or avoiding a loss (e.g. survivor wins). In these cases, illegal moves are usually regarded as a loss, but illegal moves are due to procedure and rarely set by mechanic. But there are illegal moves that are placed in the rule mechanic for various reasons, usually to prevent a drawer.
Some games have asymmetrical or differing goals. A common theme is to have the goals as polar opposites of each other, e.g. for one side to accomplish a goal and the opposing side to thwart this goal.
The drawback of this kind of endgame condition is that one side might have an advantage by having an easier goal, ways of countering include handicaps, preparation moves and in some cases, hiding one's goal from their opponents. These usually rarely apply when the opposing goals are the inverses of one another, such as the more/less goals in Libra (note that sides are decided by bid in this game)
Some games can have multiple winners, a tie. The rules set whether this is allowed or if other measures are needed to break such ties. If the tie needs to be broken, the play can either continue or be broken by another criteria.
Draws may be caused by rule, whether due to lack of a win or loss even after following all rules or by explicit statement. Chess has a few of these: Stalemate is an explicit statement (some other variations stalemate is a win), the 50 move rule as a stop to avoid prolonging a dud game, while the perpetual check condition is a mix of the two.
Some games can never draw, such as Hex. This is a drawless game by design, while there can be drawless games by rule. An example is an attempt to create a connection game on a rectangular board. A classic way to dealing with it is not to allow any checkerboard like patterns.
Drawless games will have a defect of a player always incurring an advantage by virtue of someone always winning, usually the first person to move. Methods to curb this include handicaps, adding a pie rule or playing multiple matches, usually a double round robin.
Sometimes, designers don't bother with dealing with the draw when such an outcome will rarely occur. Practically, this is not an issue unless it's a match between strong players.
This is as much as I can make out of how things happen at the end of a game, whether this is useful or not is up to you.
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