The answer is impossible as it is, because, as you suspect, this differs a lot for different goods.
Some goods can be reduced to their substance. If I steal the Jules Rimet Cup, I can melt it down, and sell the gold. I will waste the artistic labour that was imparted on it, but basically I will be able to sell its remains for the market price of gold. Being gold a very valuable material, this probably means most of the market price it would sell for in an auction. If it was made of tin, however, even though I could still melt it, it wouldn't be a good deal, because the market price of tin is quite low. In this case, the artistic labour would be worth much more than the tin, so melting it would destroy most of the value. In such a case, the cost of the theft might be more than the perspective price of the stolen item.
In such cases - which is the case of most works of art -, the piece would have to be sold as it is, and then the problem would be finding prospective buyers. Who would buy a decorative item that cannot be displayed publicly? There certain are a few collectionists out there that would pay for that, but they are very few, and contacting them would probably be very difficult, at least for your average thief. And so, such thefts are most probably done at the instigation of the 'buyer', who would probably be more accurately described as an employer. In this case, the price will resemble more a (very high) wage. A given price is fixed by the instigator, and thieves will accept it, or not, according to some cost/benefit analysis.
In still other cases, such as old but not remarkable automobiles, the reducing of the stolen part to its constitutive parts might actually add value. Possibly the start motor of a 1970 VW beetle is more valuable as a separate item than as part of the original car - especially when those items are no longer made by the original manufacturer, and yet there is still demand for them. In that case, the disassembler will be able to sell the piece at, or near at, its market value, making him able to pay the thief a considerable part of such value. But what part, this is difficult to assert, except perhaps by studying police records of solved car thefts.
Yet other goods considerably lose value if they are broken down. A gem's value, for instance, grows exponentially with its size; cutting a diamond into two smaller ones results in two gems that are each worth much less than the original diamond. So there is a trade-off here, between the remarkability of the diamond and its sellability. If the stolen gem is huge, and consequently remarkable, it probably can only be sold in the same conditions as a work of art: very few buyers, who will rather instigate the theft than wait for an occasional thief to steal the item. Otherwise it has to be cut into pieces, greatly reducing its value; so the cutter will be only able to make a small fraction of the price of the original gem, and consequently the thief will be very underpaid (moreso considering that the cutter, in such a case, will have to work quite a lot). If the gem is small and unremarkable, it might be sold as a whole, at near its market price (or perhaps even taken to the pawn shop).
So, sorry if this is a quite incomplete answer, but I hope I have at least helped clarify why it varies a lot, and explain a few variables for such variation.