What happens if an LM2576 voltage regulator fails?
But what will happen if LM2576 stops working?


Many results are possible; components can fail in different ways.


  Is that possible that it could damage my mobile phone?


Yes, that is possible.

Also note that your prototype shown in your photo does not meet the recommendations shown in the LM2576 datasheet regarding the component layout. Therefore it might behave badly, have poor output regulation, cause EMI-related problems for nearby devices, oscillate until the LM2576 is damaged, or other behaviours. Personally, I would not plug my mobile phone into that board :-(

Switching regulator design is harder than just using the correct components, because component and wiring (e.g. PCB) layout is also critical, as explained in the datasheet. Perhaps you should considering buying a suitable pre-built regulator from a reputable supplier?