It was one of those ridiculous laundry issues. A thin cord from a pair of athletic pants had snagged on one of the tiny holes near the back panel of the drum. It wasn't totally jammed, but the plastic tip was definitly wedged in, and just pulling on it did nothing.
I spent twenty minutes trying to wiggle it free, but that only made things worse. The trick was realizing I couldn't force it out. Instead, I found a pair of needle-nose pliers. Gently, I managed to grab the string right where it entered the perforation, and then I carefully teased it back. It popped right out without damaging the tip or the drum itself. It was honestly just stubborn. Glad it's sorted now.