Does an End Game automatically become a Draw at some point?

Does an End Game automatically become a Draw at some point?

E.g., after a certain number of moves where no piece is taken or whatever.

Many thanks - Sam.

After 50 moves and no one is making progress.

Yes, the 50 move rule ensure the game will end.  If no pawns are pushed or pieces are captured for 50 consecutive moves, then the game is declared a draw.

https://www.chess.com/terms/draw-chess#fifty-move-rule

Thank you Cee and Alramech. 

P.S. Good 2 c u again Cee.

You too Sam!

Yes. And also, there are some position in the endgame that is completely a drawn position if both players do not blunder.

Like the rooks and kings endgame. If there is no pawn on the board, the game is a draw, except your opponent clearly blunders his rook. There are several of such positions. 

King and Queen vs. King and Queen is a draw.

King and Rook vs. King and Rook or King and Queen vs. King and Queen would certainly be a draw unless someone makes a huge blunder. King and Rook vs. King and Queen will also often be a draw based on the 50 move rule. It's really really tough to force that win unless you've specifically practiced it--as is also the King and knight and bishop vs. King. Of course, insufficient material is also an automatic draw. If both sides are left with, say, one bishop or one knight, it's a draw.

The threefold-repetition rule says that if a position arises three times in a game, either player can claim a draw during that position. 

Thank you very much.

#1
"9.3
The game is drawn, upon a correct claim by a player having the move, if:
9.3.1
he indicates his move, by writing on the paper scoresheet or entering move on the electronic scoresheet cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move which will result in the last 50 moves by each player having been made without the movement of any pawn and without any capture, or
9.3.2
the last 50 moves by each player have been completed without the movement of any pawn and without any capture.
9.4
If the player touches a piece as in Article 4.3, he loses the right to claim a draw under Article 9.2 or 9.3 on that move.
9.5.1
If a player claims a draw under Article 9.2 or 9.3, he or the arbiter shall stop the chessclock (see Article 6.12.1 or 6.12.2). He is not allowed to withdraw his claim.
9.5.2
If the claim is found to be correct, the game is immediately drawn.
9.5.3
If the claim is found to be incorrect, the arbiter shall add two minutes to the opponent’s remaining thinking time. Then the game shall continue. If the claim was based on an intended move, this move must be made in accordance with Articles 3 and 4.
9.6
If one or both of the following occur(s) then the game is drawn:
9.6.1
the same position has appeared, as in 9.2.2 at least five times.
9.6.2
any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence."
https://handbook.fide.com/chapter/E012018 

There are also some immediate material draws:  K vs K; K+B vs K; K+N vs K; K+B vs K+B when both bishops travel squares of the same color.  I those positions checkmate is impossible even if one player is trying to get checkmated.