Your temperature transmitter should detect the presence and condition of the sensor, and alert you to RTD sensor failure. If the sensor hasn’t been installed or doesn’t work properly, the transmitter will go into RTD failure mode.
What to do when an RTD fails?
If you think your sensor will fail or has failed, you may need to upgrade your sensor, for safety, if nothing else.
You could also install another sensor on the application as a backup. If you have a problem with the first sensor, then the transmitter will switch automatically to the second. It’ll also send a diagnostic about the failure on the first sensor.
Whatever you decide to do, I suggest you do it as soon as possible. There are many good alternative options, and while they all may cost more, you have your safety issue to consider.