If I have understood the question properly, there is no simple answer, especially without some knowledge of the application, the sensor types and the key concerns.
What can be done could depend on the transmitter type, manufacturer's defaults, available outputs, sensor and control circuit sophistication, the application, capability, potential for user configuration and the actions required.
Sensor capability depends on output type and whether it is a smart sensor or not.
If it is a 0-5volt or 0-20mA output then if it fails, there will be no indication as to whether it is a power supply failure, a process excursion or transmitter error.
With 4-20mA and it is not a power failure, it is often the case that it will be configured to default to 2mA as a fault alarm.
Faults can be intermittent, transient or continuous and due to a variety of causes.
But what fault?
It could simply be a general alarm for any one of a number of fault conditions that require investigation.
These can include out of range process variables, rate of change alarms, system or checksum errors, input failures, calculation failures and so on.
It is necessary to consider what faults could occur, what could happen as a result and what action should be taken when there is a fault and if this action is different dependent on the type of fault.
In some smart sensors there may be transient error configuration that allows the option of defaulting to the last good value or defaulting to a pre-set value for a brief period to allow for the sensor to recover from a transient process variable error.
In feedback control applications faults can create unfortunate control responses.
If it is a level transmitter that fails, what do you want to do?
If it is a boiler filling then you might want to maintain water flow until someone can investigate and decide what extra action is required. If it is a tank filling operation you may want to shut down filling to prevent overflow. Which is the appropriate response? It depends on the activity and perhaps on where you are in a particular operation cycle.
The real answer is to assess the application.
Deicide what fault conditions could occur.
Decide what action should take place in each of the fault conditions and then see if you can find a transmitter with the necessary configuration or if you need some kind of ancillary controller to manage the fault condition.
JMW