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The relay must stay in its state. When an electrical impulse is sent to it, it should switch its state and should maintain its status.

So I am really curious about it. Is there such a thing for saving lots of power?

Yes, they go by various names such as a bistable relay, latching relay, or impulse relay. Common in small (telecom style 2A or less) and also some power relays have this function.

There are various methods of actuating them, the small ones typically have either two coils (pulse one coil for 'on', pulse the other for 'off') or single coil (reverse polarity pulses for on vs. off).

Some of the power ones are alternating (pulse on, pulse off). One application of the high-power relays is for electrical metering where the power can be remotely switched off in case of bill non-payment by the customer.

But latching relays continues to draw energy for coil inside of it after one o hit the button ...

You are getting confused with a relay circuit that electrically latches the relay on. A latching relay is bi-stable. It has two stable positions. It uses two coils to switch it - or one but you have to reverse the polarity.

Figure 1. A latching relay will stay in the last energised position when power is removed. Source: Homofaciens.

Example of a mechanical latching relays can be found in early telephone exchanges.

The stepping relay, or Strowger switch, was used to establish a switched circuit through a telephony exchange. Power was used to advance the relay for each click of the dial pulse, but once the digit was complete, the switch held its position.

More advanced exchanges used crossbar switches which connected more points in less space. These were also latching and did not require power to maintain each specific connection.

In a way, each cell in non-volatile memory (NVRAM) is a latching relay. Each cell stores its state when power is removed and uses no power to remain as it is. Only when the state is changed does the "bit" use power.

In many implementations of NVRAM, the state is stored as an island of electrical charge stored within an insulating framework. The stored charge influences the ability of current to flow through an adjacent semiconductor channel.

If you want a readily available example, GE makes a line of latching relays called RR7. They are used for commercial lighting. They work exactly as you wish, and run on 24 VAC or DC or voltages in that ballpark.

Also the Half-Bridge FET Relay only consumes power during the switching transition which is proportional to the Q charge on the Gate input and Drain output during switching. However, in normal operation, they are used to also vary voltage with PWM which draws switching power at a higher rate. But the high side of the dual half-bridge or "full-H bridge" bridge is used to change directions of current after flow has stopped with very little power.

However, IGBT's with FET input are more suited to AC line voltage and require costly protection for line faults or surges.

Similarily , the Thyristor family of parts only need a pulse to latch-on for the next cycle.