digital output

is it to program the state of the output in case the plc fails or stops? is there a ob that runs in case of plc stops ?

No and no. Design your system so it is safe in a power-failure condition.
In a power fail condition, all outputs are off.

(Assuming Siemens here as mention of OB)

There are failure/diagnostic OB's that allow you to save information on the cause of a PLC crash and in most cases, once programmed in will not crash unless you tell it to.

Really the decision is down to you on how critical it is to stop the PLC on an error, this should be determmined by what the PLC is controlling.

As mentioned above the hardware should always be designed to fail safe.

As an indication on the front of the panel, you could include a lamp controlled by a PLC output, set the PLC to always turn on this lamp. If the lamp is off the PLC has stopped.