Yes, it's called a memory leak and usually results from programming errors. There is programming libraries to test against these. It usually comes from someone reserving computer memory for something and not freeing it up. I hope they fix it soon.
If you're not moving it's most likely either in the network program-code of FFXIV or in the display program-code for everything happening around you. There is little you as a user can do against it except opening and tracking a ticket or posting to the forums for now.


https://en.wikipedia.org/wiki/Memory_leak