I'll take a stab at it, although I know nothing about goji plants. If the roots feel soft and mushy, than I'd say yes, they have rotted, especially if the main stem feels soft near the rootball. Perhaps the roots dried out at some point.The plant also looks like it's lacking light unless that's a grow light. The light also looks a little close to the plant??? Possibly causing too much heat??? It also looks like it's overpotted.
