This could be so many things.
A layer that was turned off so you didn’t see it in AI may come into AE and be turned on, especially if its a background that spans the whole comp.
It could be a compound mask or clipping mask not being interpreted correctly thereby showing you the AI mask instead of whats inside the mask.
It could be a counter inside a letter not being “see through” and instead become a solid. So if you had a large “O”‘ acting like a window, all you might see is a solid the color of the “O” and that might cover everything behind it.
It could be just the way you have layered your AI project, or the version of AI file vs the version of AE file. I find if you bring a newer Ai file into an older AE file, often groups are broken up into their sub components and each of one those becomes a layer (similar to opening a new AI file in a old version of AI.
Without seeing the original illustrator file it’s hard to say.
No all that being said, the title of the post is what I responded to above, but if you are copying the paths to shapelayers then it might be something else. Check that paths are closed or open as they were in illustrator. I’ve seen lots of paths come in closed where they were open in illustrator.