Max

This was in Mörk Borg, a system known for its absurdist and merciless atmosphere...
The player joined later, in the middle of an ongoing fight! He was quickly assigned a character: a wizard.

On his very first turn he tried a spell, but it went terribly wrong! Instead of a fireball he conjured a tear in reality, and immediately fell into another dimension to be trapped there forever.
The wizard stormed into the fight and immediately fell out again. After one turn the player already had a new character...

"Game Master, can I [...]?"

Yes! Always try anything, I love rewarding player initiative and creativity. That way you create a story together that belongs to everyone, and often even more chaotic (and therefore more fun) than I myself could imagine.

.. a session in which a heart-stopping chase and a sorrowful ending coincided.

The players barely escaped an advancing shadow that overran their fort! Everyone in the fort was swallowed, and most of the players just managed to flee into the forest. But one of them fled into the tunnels, deep underground.
After a long walk she encountered an old goblin in the deep tunnels at the end of his life. She stayed with him in his final moments, and the goblin, who had never experienced such charity in his life, was intensely grateful to her.
Then the tunnel was silent.