I purchased a rock-hard, six-pound pork shoulder at the farmers' market on Sunday and have been thawing it in the fridge since then. As of this afternoon, it's still not completely thawed, and I'm starting to wonder if the thawed outer layer of the shoulder might go bad before its inner layer thaws. How long can I continue to safely thaw it?
Unless your fridge is above 40 F (4 C), it won't go bad. I've had large frozen turkeys take 4 days to thaw before. Just use it once it is fully thawed, don't let it sit around thawed for several more days.
There's no food that I'm aware of that goes bad in the time it takes to thaw it. The stilltasty link below shows 3-5 days for refrigerated meat, and 4-6 months for frozen. Transitioning from frozen to thawed though, I generally count on defrost time + 2-3 days.
If you want to thaw it faster you can always use the cold water method. Simply place it in a sink full of cold water (submerged) and change the water every 30 minutes. The rule of thumb for turkey is 30 minutes of thaw time per pound. I imagine pork shoulder would be similar, maybe a little longer?