The steel goes to the highest bidder to be melted down and rolled into new stock.
When a ship is scrapped, it's merely the end stage of a fairly long process. After the ship is removed from service, the hull is stripped of any usable fittings and parts, some of which are re-used such as the appintments and furnishings on the
Olympic. This can happen either befor or after sale to the one who bids on the contract. Once the ship arrives at the breakers yard, any remaining fittings are stripped out as the hull is cut up into managable chunks which are removed and cut up for removal to the smelters.
This, BTW, isn't as easy as some might think as stability becomes an issue if the hull is still afloat. The engineers have to arrange for sections to be cut away in such a fashion that what's left doesn't do something rather embarrassing...like roll over and sink at the pier.
This isn't much of an issue if the hull is deliberately grounded like what they do at Alang. What
is an issue are health and safety concerns...especially when knicknacks such as toxic material (Asbestos lagging, PCBs, residual fuel oil, paint being chipped away) have to be removed.
In western nations, there are some
very strict regulations on how it's handled and disposed of. A shipbreaker can literally go out of business dealing with these problems, and an example of that is the company which tried to dismantle the USS Coral Sea. This is one of the reasons why contracts are let to places like Alang or China and Taiwan.
Eventually, what's left are a few sections of the ships bottom which are in turn cut up and removed until nothing is left.