Go ending. Why do players stop?

Question

I'm learning the game GO. I see that after the players have made a lot of moves, at the end of the game, there are several visible territories for black and for white. But I don't understand, why does the game stop there. For instance, I think that if white plays inside black's territory, black will be forced to play inside to capture it and when doing this, he will place his own stones in his territory, which makes his territory count lower.

What prevents them from playing inside the opponent's territory?

Answer 1

This is anwered by 'gennan' here:

Why players don’t try to occupy opponent’s territory with living group of stones at the end of a game?

When using territory scoring (points for empty intersections inside), you also get points for dead opponent stones left on the board when the game finishes. Dead stones are understood to be removed from the board and added to the prisoners between passing and scoring, so you get points for the vacated intersections underneath them as well.

So if white places a stone inside black’s territory that ends up being dead, black gains a point. If black responds by putting a stone inside their own territory to defend, black loses a point again. So then the result would be no change in the net score.

In a contest, this might be considered to be stalling or time-wasting, when the game is effectively over.

Answer 2

As Weather Vane explained, if you play in your opponents territory and your opponents responds with a move inside their territoy this is point neutral. This basic principle is used to resolve disputes about whether a certain area is territory or not.

If white claims a certain area as her territory and black contests this, then white can just say: go ahead play in there and try to make a living group or capture some of my stones. If black is correct than further playing will show that and the game wasn't finished yet. If white is correct it doesn't cost white anything to let black try and as long as white has to respond to every move by black this doesn't change the score. In summary this means if there are any disputes you can just play it out and neither player has any reason to refuse this.

So in that sense players are even encouraged to play in their opponents territory if they are not 100% sure that it is their opponents territory.