Below is an image taken from the Electric Fields entry of Encyclopedia Brittanica. The general rule for drawing field lines supposes that the lines are drawn starting at the positive charge and terminating at the negative charge. In this image, where do the lines emerging from "behind" of the charges end? If a point charge is placed on this line, would this mean it would only be affected by the charge it is placed behind? 
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$\begingroup$ What do you mean by "behind" of the charges. The image is obviously the projection of three dimensional field lines. $\endgroup$– Bob DJul 6, 2022 at 19:11
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$\begingroup$ @BobD I mean the field line that bisects the image horizontally, specifically the region that is not in between the two charges. $\endgroup$– PiksikiJul 6, 2022 at 19:37
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$\begingroup$ So like looking at the positive charge with the negative charge not visible behind it? $\endgroup$– Bob DJul 6, 2022 at 19:48
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$\begingroup$ @BobD yes, that's what I meant $\endgroup$– PiksikiJul 6, 2022 at 21:01
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$\begingroup$ The line leaving the image on the left is running around the whole universe and enters again on the right, ending on the negative charge, like in pacman. Sounds funny, but is actually the extreme case. Every field line starting here on one charge ends on the other (if you assume that there are other charges around, outside the image, they can end there as well...). $\endgroup$– Charles Tucker 3Jul 6, 2022 at 21:01
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1 Answer
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The general rule for drawing field lines supposes that the lines are drawn starting at the positive charge and terminating at the negative charge. and you have found exceptions as there are with the electric field diagram below which has a neutral point (no electric field) at point $X$.
What you must remember is that the field lines that your draw/imagine are aids to help with visualising electric fields.
Electric field lines have no thickness and, without resorting to line density ideas, do not show changes in electric field strength along their length.
In your example and in mine some lines just peter out.
