Hello ,
I want to measure ac current with acs712 , but what happens to the circuit if the sensor broken down ? Will it stop working or continues ?

 

if the sensor broken down

There is more than one way to breakdown. Most likely there will be current flow in the load.

 

Looking at the datasheet the part should survive a current on the sense path of up to 5x rated max current. Above that there is the risk it will fuse internally and stop current flowing in the sensed circuit. If you are concerned about the load losing power during this obvious overload situation shunt the ACS-712 pins with two really big honking diodes wired anti-parallel. When the ACS-712 lets its smoke out the big diodes will help something else catch fire or, if you are lucky, a fuse blow.