The intersection marked with a triangle is usually called a teire: an intersection within Black's territory, but which Black will have to fill before the end of the game.
The description of what precisely will happen varies depending on whether the game is played face-to-face on a physical go board, or on an internet go server.
Face-to-face with a physical go board
During a face-to-face game, you can expect Black to play at the triangle before passing, and White will reply by playing at the square.
During face-to-face games with physical go board and stones, players typically fill all the dame, even when playing with Japanese rules, because it makes counting easier. Unfilled dame are extremely distracting when counting and can easily be mistaken for territory in the counting phase, when rearranging territories into rectangles. So players always fill dame.
However, when playing with Japanese rules, the dame-filling phase is sometimes played somewhat-separately from the "real" game. For instance, if the game is played with a clock, then players might pause the clock before filling the dame, and they might also fill the dame out of order. Since Black should not play the dame marked with a square before playing at the triangle, and since White would put Black in atari if White played the dame with the square before Black connected at the triangle, Black would probably still play the triangle during the game, before the dame-filling phase, just to avoid any ambituities. And then the players would pause the clock and fill the dame, including the square.
When playing online with Japanese rules, the players most often don't bother to play dame, because counting is done automatically by the computer, and territories are typically coloured, so neutral points are not too distracting nor confusing.
However, what happens around the triangle intersection will depend on the go server and the counting algorithm used by the go server.
For instance, the go server KGS correctly detects simple teire points like the triangle, when playing with Japanese rules. So, Black would not receive a point for the triangle intersection, even if it is unfilled. If both players know this, because they have played several games on KGS already and are familiar with, and confident in, the scoring algorithm used by the server, then it's very likely that Black will pass without connecting at the triangle. Likewise, White will pass without playing the atari at the square.
However, if playing on a go server that doesn't handle teire points as well as KGS, or if the players are not entirely sure how the go server handles teire points, or if one or both of the players are driven by the habits they got when playing face-to-face games, then it is very likely that Black will play at the triangle; and if Black doesn't play at the triangle first, then White will play the atari at the square, to force Black to connect at the triangle.
So, it's a big if. The triangle point will only remain unfilled if the server correctly detects teire points when playing with Japanese rules, and both players are familiar enough with the server, and not driven by their habits from face-to-face games.