FIG. 1 is a front perspective view of a handheld electronic device case; FIG. 2 is a rear perspective view of the handheld electronic device case; FIG. 3 is a rear elevation view thereof; FIG. 4 is a left elevation view thereof; FIG. 5 is a right elevation view thereof. FIG. 6 is a front elevation view thereof; FIG. 7 is a bottom plan view thereof; and, FIG. 8 is a top plan view thereof.