Some Pandas came with a full size radio, which was factory fit, and tied into the vehicle computer, so won't work in another car unless codes are entered.
Other Pandas came without, but were usually fitted with a standard size unit, either by Fiat, or the dealer prior to sale. Those should work properly.
A few, might have been delivered without a stereo, or had one replaced later. These are often wired incorrectly.
Older vehicles used multiple wires in the power plug, one was permanent live, another was ignition switched live, plus others for earth, electric aerial, speed input (nav), reverse (nav) and lighting (display dimming).
These Pandas only have 4 wires to the stereo from the car. These are permanent live and earth, plu stwo tiny wires which are the CanBus data cables. These two must not be connected to aftermarket stereos, but often are. Mostly the wires do nothing, but worst case is they can damage the car body computer. With the factory stereo, the CanBus privides signals for lights, speed, reverse, and ignition on/off.
My guess, and this is usually the case, is that the stereo is aftermarket, and only the permanent feed and earth are connected, so there is no ignition connection.
To do the job properly, a connector module should be used, like this one:
https://connects2.com/Product/ProductItem/CAN-01.3
That interprets the CanBus signals and sends analogue signals to the head unit, giving ignition on/off and lighting signals, as well as speed and reverse if required. (I've had one of those adaptors for years, previously fitted in various Corsas, two Fiat 500s, and then my Panda since 2010.) Expensive, but oes the job properly.
Many people opt to save money, and take an ignition feed from the 12v socket, if fitted.
If the CanBus wires are connected to the head unit, they need to be disconnected, and insulated.