When you leave the minecart for what reason soever, you will be placed outsite of the fence line, with no chance to get back in the minecart.
Only destroing the fence or placing a block to jump over the fence helps.
Related issues
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Well very clever, but I place the fence because it keeps the mobs away from walking on the track and also my self save from shooting skeletons. Also I don't want tracks that are high in the air, messing up the landscape

It does happen sometimes (not related to the fence), but I'm not sure how this is a bug. In my case I have the final line hitting a wall (with a button, last rail is powered) and a sigh on the RIGHT side (track is W<->E, wall on W, sign on N) and when I leave the cart, it places me on the block NW, which is the farthest possible lol (I half expected it to place me on the rail before it, E of where the card is, or at least on the adjascent free block at S, but it put on on NW, go figure)

Priority minor is not adequate.
Where to patch: (using MinecraftCoderPack class and methods names)
Entity.java
public void unmountEntity(Entity par1Entity)
There are two loops (on X and Z axis)
for (double dX = -1.5D; dX < 2.0D; ++dX)
for (double dZ = -1.5D; dZ < 2.0D; ++dZ)
inside these loops checked for emptiness eight blocks around player and one_level_up - see getOffsetBoundingBox(dX, 1.0D, dZ);
Block above the fence is empty, and player placed in relative coords (-1.5, 1.0, -1.5) to the north or to the west. It is exactly on wrong side of the fence.
Solution:
1. Add outer loop for (double dY = 0D; dY < 1.5D; ++dY) // optional, but i think it is normal to exit from minecart to the ground, not into air.
2. Make loops bounds smaller: for (double d = -1.0D; d < 1.1D; ++d) // important. With this values exiting is also on sibling block, but if it is something like fence - player will stand on it.
P.S.: Sorry for ugly english
Also it is duplicate of #MC-1489

I made a video, its in german but it shows the error in the first 5 min. Maybe this helps understanding it.

Duplicate of: MC-1489 - Please use the search function to see if your bug has already been submitted.
Currently 27% of tickets are being closed as duplicate.

Thx, when i searched i was simply too exact. "minecart leaving fence" was my searchterm 😃
Well, Don't Place A Fence Then.