Hello Liam
It depends upon how you remove the person from your marketing list. There is currently a CRM bug that causes the nurture to not recognize if you remove a list member using Manage Members > Remove Using an Advanced find or Manage Members > Evaluate Members using Advanced Find. As such, the person would keep going through the nurture if you removed them using those options. If you remove the list member through another method, that will cancel the nurture for the person at that point and adding them back to the marketing list would cause them to restart the nurture.