Nobody knows what's real, and you can do worse than thinking about an analogy involving sheets of paper, so let's just fix that analogy.
as a straight line on a paper reach a hole on the paper
But in this analogy, isn't the straight line possible to continue into 3D (continue down the paper)?
Don't think of it as "punch a hole into a sheet of paper". Your image should be more of a very deep, in fact infinitely deep well made by the sheet of paper. It goes ever on and on (in the 3D space into which the paper is embedded).
In this analogy, your line does not have to end, it also does not have to re-appear on the other side of the well (which is infinitely deep), and it will not leave the paper either, and nothing in particular will happen to it.
On a side note, this analogy extends to give an idea how wormholes could be imagined - instead of an infinitely deep well, curve it around and attach it to another bit of your paper...
Again, I have to stress that these are all just imagery or illustrations to guide your mind into having anything to think about. It would be very weird if the complex real world would function as simply as a sheet of paper.
By the way, I like another analogy more than the paper: a reasonably big lake of water with fish with it and a hole in the middle through which the water can flow out freely. Very near the hole, the water flows faster than the fish can swim (="speed of light") with all the consequences you can imagine. Obviously, nobody knows what happens to the fish when it is finally sucked in. :)