As I understand it, standard stop loss orders at a fixed price are sent to the exchanges. They are visible on the order book as plain vanilla buy or sell orders not as stop loss orders per se. Complex stop loss orders may be a different story.
There are a dozen or so exchanges in the US and each exchange supports different types of orders. Algorithms are complex broker orders which may be supported by the exchange (for example, an Iceberg Order). If not supported by the exchange then the order is held at the broker until triggered rather than being constantly cancelled and replaced on the order book.