What do you call a relay that self-opens on power loss?
It's called a "relay". There is nothing special here. Normal relays are held in one state by mechanical spring action when the coil is not energized, and in the other state when the coil is energized.
A relay being energized and power going away is no different from you switching it off deliberately. Either way the coil stops producing a magnetic field, and the mechanical spring returns the contacts to the unenergized state.
There are such things as bi-stable or latching relays. These mechanically stay in the same state they were last driven to. Of course driving them is no longer as simple as energizing or not energizing a coil. There are two possibilities. There can be two coils, each used to drive the relay to one of its states. Or, the magnetics can be polarized so that current polarity thru a single coil determines the state the relay is driven to. One way or another, there needs to be at least three different driving states.
Latching relays are much less common, and any such relay will be clearly labeled as such. Just a "relay" has a coil that is either on or off.
For normal (non-latching) relays, contacts are classified as normally open (NO), normally closed (NC), and common (COM). NO and NC refer to the switch states when the coil is not energized. A SPST relay is the simplest type, since there is only one contact and therefore two output leads. This type must be specified as normally open or normally closed. If you want the relay to "shut off" when power goes away, then you want a normally open type.
Many relays have SPDT outputs, or multiple of them, like DPDT. In that case, one of the ends is normally open and the other normally closed. These flip state as the coil is energized. The center contact that flips between being connected to the NC and NO leads is the common.
It's a relay with a normally open contact. Relays can have Form A (normally open) Form B (normally closed) or Form C (changeover) contacts, which act pretty much as you would expect from the names. "Normally" covers the state when the power is not applied, of course.
Relays with moving contacts that bridge two fixed contacts (as your schematic seems to indicate) are often called "contactors". They are typically designed to switch relatively high currents, and the high power contacts are invariably normally open. Sometimes they have low current auxiliary contacts that may be normally open or normally closed (or changeover). Relays, on the other hand, typically have a flexure or wire that carries current. In cases where the flexure doubles as the spring, overloading can cause the relay to fail 'on', which is usually considered quite undesirable.
In some cases, relays are wired in a self-hold configuration so the power to their coil is maintained through the relay's own normally-open contact. A momentary contact closure bridges the NO contact and pulls the relay in. This configuration is frequently used in machine tools and similar devices where you really want the machine to shut down and stay shut down in case of a power failure and subsequent restoration of power. This is not an inherent feature of the contactor or relay, however, it's just a way of using the component.
Related but not necessarily what you're looking for:
Sometimes, relays for high power switching are known as contactors.
Another term used in industrial machinery for motor control is "NVR Switch" (for No-Volt-Release). These are used when you want a machine to return to a safe (unpowered) state in the event of a power failure.
They usually incorporate circuit protection (overcurrent protection) as well as start and stop buttons, possibly wired to additional remote stop buttons.
Internally, a NO (normally open) relay holds itself closed until either a STOP button breaks the connection to its coil, or loss of mains power allows it to open its contacts.