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Flagging in a position that cannot be won

I have always been told that if you run out of time and there is a possibility to lose the game. Either by playing the best or the worst moves possible you lose the game. Isn't also the opposite true: that if there is no possible way to lose or win a game and time runs out it should be a draw? For example in this game lichess.org/xXmXAEBz?pov=lorenzof98 there are only pawns and kings left. No pawn can be moved and such pawns control all the squares needed for the kings to go behind the enemy pawns and capture them. In fact, whether this endgame is played by Carlsen and Caruana or two monkeys the result will be a draw no matter what. Shouldn't this be a draw even if my opponent ran out of time?
At first glance, in theory, that should be a straight-up draw. But for the 50-move rule against the time control. In this case, time ran out (control) before 50 moves.

On the other hand, LiChess is quick to proclaim draws based upon repetition (i.e. if one or both players have a setting enabled to such effect; I can't see your settings, nor the other player). Based upon the way most of LiChess' rules operate, this probably should have been a draw, and sufficient (programmatic) controls are not in place to detect the lack of game progress and repetitious nature of a drawn position. Maybe enable the condition in your settings to force a draw?

Will be interesting to see how LiChess programmers handle a condition like this.
#2 Said everything, I guess

But it would be very hard to program something like this. There is the 50 moves rules for that, but when there is no increment... You either respect your opponent and agree to a draw or play it on to win because you have more time.

By the way, why did your opponent give you more time ? Between 62... Kd8 and 63... Ke8 you gained 15 more seconds on your clock...
Check your settings, the condition might be handled...

Go to your user profile "Preferences", then "Game Behavior", and check the "Claim draw on threefold repetition automatically"

I have mine set to "Always," but "When time remaining < 30 seconds" is acceptable, IMO. Irrespective of your setting, if 3-fold repetition is caught, the ability to claim a draw should appear (if you're not in zen mode). If I remember correctly, if you don't have this set, the option could disappear if someone breaks repetition. But, in a position like that, the LiChess systems may catch the lack of game progress all pawns blocked, and king-moves only and declare a draw if one or both players have a similar option set.

If as #3 said: You were given 15 seconds, this should almost definitely trigger a condition to check for advanced conditions (or, positions) like this. (Otherwise you could end-up with 300+ move games; on 3-minute time control. Just keep adding time to each other. That's obtuse if not abuse.)

Again, except for time control. That's where things get weird with the 50-move rule and completely stalled positions like that.
Of course it is a instant draw at move 59 using FIDE rules. But it cannot be coded.

As simple as that.
The fix is to play with increment.
I've never played a real-board chess tournament, so could someone clear this up for me please?

If I call the arbiter over with 55. axb5 on the board and point out that it's impossible for either side to win, regardless of what moves are played from then on, is the game ruled as a draw? Or do we have to reach three-fold repetition or the fifty-move rule?

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