Possibly bearings or worn out of adjustment. How many miles has it done? has it got oil in it.
Thing is how long has it been run like that, as it may have caused damge to crown and pinion, if it isnt already damaged.
Usually my rule of thumb with diffs is; If it whines, then its knackered, the crownwheel and pinion have probably worn through the case hardening, and basically its beyond the point of any usefulness in a road going car.
If it rumbles then it may be bearings and/or needs resetting with new shims and preload. Not an easy job to get right from a DIY point of view.
The obvious thing here in both cases, is to check the halfshaft bearings first as these are cheaper and easier to replace, but can often be over looked people thinking its the diff making the noise when in fact it isn’t. Been there got the t shirt!!
