Does a robotic lawn mower sense that it is outside the perimeter wire? If so, how?
Expanding my comment into a tentative answer.

There is a low power radio transmission system called the "inductive loop" which uses a large loop of wire as an antenna. It provides good signal strength within the loop, and virtually none outside.

This allows induction loops to provide radio coverage e.g. within a building such as a concert hall or theatre or hospital with virtually no interference to other spectrum users outside the building. One common use is to help hearing aid users at the theatre.

But its characteristics are just about ideal for confining a robot within a space defined by a perimeter wire. Transmit a simple code at low power. If the robot loses the signal, it must stop. Simple as that.

Now I don't know if any specific lawnmower uses this system, but it's the most obvious candidate.