To fix that single prim, you do not have to unlink the entire object, however. Simply follow these steps.
1) Open the Edit float and select the linked object.
2) Check the box to edit individual prims. (Last box in the list, I have forgotten the actual name, but is self-explanitory in its title)
3) Click on the prim you wish to edit, so that only that prim is highlighted.
4) Go into Tools and select "Unlink" That one prim will now be unlinked from the whole. All the other prims should remain linked.
5) Edit the single prim as desired (be sure to uncheck the box to edit individual prims. leaving it check prevents editing as the edit programming still believes it is only a "piece"
6) When done editing, highlight the single prim, then highlight the other linked object. The reason for selecting the linked object second is that the last object linked is always the root prim (the prim highlighted in yellow instead of blue. This prim controlls the center of mass of the object and is also used in various scripts for referencing). If you link a prim to a linked object by seclecting the single prim last, you will change the root prim to that prim.
Done, or go back to Step 1 to edit another prim ^.^
Take care, and happy building,
~Jessy