I've never seen anything to 'fill' the remaining space, and I would advise you to avoid this so that you don't damage the pins. There are other design features that should ensure a good and accurate fit.
Remember, a "tight" fit does not necessarily mean a "good" fit. In this case the pins are spring loaded to provide a good contact with the card-edge connector, and it doesn't typically feel "tight" - especially with the lower pin-count cards.
The key in the connector should ensure correct horizontal alignment, such that the pins and pads aren't misaligned:
Additionally, the card's bracket should provide a fixing hole so that the bracket can be attached securely to the chassis / enclosure - to ensure that the card doesn't come out of the socket:
The bottom of this bracket should fit into a slot in the chassis to further ensure correct alignment.
This side-view graphic, courtesy of Samtec shows the spring-loaded pins (I've colored the pins):
These connectors are designed specifically to mate with a 1.6mm PCB - so if the connection feels overly loose or you're having functional issues, then you could always check the PCB thickness... though a PCB of anything other than 1.6mm is out-of-spec - something that may be true for an especially cheap card.
1I have never seen anything like a spacer or plug to fill the extra space... And have never had a 8x card in a 16x slot have a poor connection. Once the card is inserted and fastened/screwed down, it certainly shouldn't move. – acejavelin – 2018-03-07T15:14:59.923