Do TI has a sub 1GHz RF trans-receiver which wakes up from the low power mode when it detects a carrier?

CC1101 has a feature called Wake On Radio (WOR), which is a duty cycled version of what you describe. CC112x and CC1200 has a feature called sniff mode which is also similar, but more advanced. Suggest to look at those devices.

The radio need to be active in order to "listen" to incoming signal so having a radio that is off all the time is simply not possible.

Thank you!
Is it possible to read "RSSI" in low power mode? So as soon as if RSSI > RSSI_threshold=> wake up for receiving

No. The radio needs to be in active mode (RX) to detect energy through RSSI. As mentioned before, you can get low average current consumption by waking up at certain intervals and check for energy. What is the application, system parameters, and system requirements?