The ornamental design for a fabrictoiletpaperstorageunit, as shown and described.
FIG. 1 is a front, left side, and top perspective view of a fabric toilet paper storage unit showing my new design;
FIG. 2 is a front, left side, and top perspective view of a fabric toilet paper storage unit with the fight front partially open, the left front being a mirror image of the right front.
FIG. 3 is a front elevational view thereof;
FIG. 4 is a left side elevational view thereof, the right side being a mirror image;