No aircraft I have ever come across, or even heard off, as any kind of auto shut-down system on the engines. If an engine shuts down in flight it is because the crew have decided to shut it down or because there has been a catastrophic failure that prevents the engine from operating.
Some turbine engines do have automatic shutdown features. This is common on certain APU's with automated start procedures,for example. A number of different switches that monitor various parameters will shut the engine down, from overspeed sense circuitry to oil pressure switches.
Some turbopropeller engines have a somewhat similar function, using an "autofeather" feature which doesn't shut the engine down, but feathers the propeller automatically if a torque loss is sensed on one engine. This is specifically a takeoff safety feature. The engine may actually be running at that time, but the system is designed to eliminate the drag of a windmilling propeller and feathers the propeller.
I've personally experienced a loss complete loss of oil in a motor, in which the engine kept running; according to the manufacturer, the engine has been demonstrated to run for a half hour with no oil. In that particular case, the failure occurred on a turbopropeller engine. The lack of oil pressure prevented the engine from "developing torque," in that while the engine was still providing power to the propeller, the propeller wasn't available to produce thrust.
Takeoff in an airplane is a little different than an operation in a boat. Generally on takeoff, we don't touch anything if there's an emergency until the aircraft is a minimum safe distance in the air. If the engine is producing useful thrust, we use it, whether it's out of oil or has some other problem. In a boat, you could use an auto shutdown circuit to protect the engine without too much concern about the dangers that an aircraft faces on takeoff; you could do more to protect the engine as your priorities may be a little different.