Can you get ObjectValue(s) to automatically update?

Simple, just make it so when the part's parent changes, it checks if it's parent is nil or not. If it is, then update the value. Here's an example:

local Part = Instance.new("Part") -- The object

-- Create & Assign the value
local ObjValue = Instance.new("ObjectValue")
ObjValue.Value = Part

-- Connect a function that fires when the part is changed
Part.Changed:connect(function(property)

	-- If the property changed is "Parent", and the part's parent is now nil, then...
	if property == "Parent" and Part.Parent == nil then

		-- Update the value to nil.
		ObjValue.Value = nil

	-- End the if statement
	end

-- End the event
end)

Hope that helped, let me know if you have any questions.