Putting half thawed joint of pork back in fridge to fully defrost?
Frozen food should always be thawed in the refrigerator no matter what, here's an explanatioon : 

frozen food put on the counter will defrost quicker than in the fridge , but bacteria activities will occur, now bacteria activities will occur no matter what, but if you keep it in the fridge the amount of bacteria will be less than if you left it on the counter. 

That being said, I would check what the temperature on the surface is, if it's between 2 and 5 degree celcius than I would assume it would be safe for consumption if you let it finish defrosting in the refrigerator, otherwise might as well throw it away because when you get to the point of completely thawing your joint on the counter, the surface will be swarmed with bacterias and will most likely make you sick.

So in a shell : temperature on the surface is key. 

Hope it's not too late !