This has been suggested to pretty far, even light-years, plus have been turned into a subspace beacon or transponder especially if damaged to aid in finding the owner either to rescue a survivor or to recover the body in the event of death. Has someone any information on how this is supposed to theoretically work? What was the max distance mentioned in Star Trek canon (or non-canon)?
Approximately 40,000 km (ground-to-ship)
Communications functions are carried out by tricorder through the subspace transceiver assembly (STA). Voice and data are uplink/downlinked along standard communicator frequencies. Transmission data rates are variable, with a maximum speed in Emergency Dump Mode of 825 TFP. Communication range is limited to 40,000 km intership, similar to the standard communicator badge.
The communicator is a line-of-sight device during away missions. Its planetside range may be improved if the magnetic field value is below 0.9 gauss, or mean geologic density is less than 5.56 g/cc.
Approximately 500 km (ground-to-ground)
The range of the communicator is severely limited, mainly due to the small size of the STA emitter and power supply. In transmissions between two stand-alone communicators, clear voice signals will propagate only 500 kilometers. This is a tiny fraction of the 40,000 km required to contact an orbiting spacecraft, so it is the spacecraft that must become the active partner in order to receive the communicator's lower-power signals, and transmit correspondingly high-power signals to the communicator's receiver.
As shown in numerous episodes, a standard combadge can reach a ship in orbit; we see the Away Teams reporting to their ship as soon as they arrive on a planet's surface to confirm their arrival.
Communicating further away than orbit requires a boost or a modification of some kind to send the signal far enough.
TNG S03E03 - The Survivors
RIKER: All right. I can't make you come with us. (takes off his comm. badge) Are you familiar with one of these? We'll be in the system for the next several days at least. If you reconsider, please contact us. RISHON: We'll be fine, Commander. We have each other.
So if everything was wiped out on Rana IV, there would be no equipment left to relay a ComBadge signal. If they are going to be in the system for several days (supposedly on there way out of the system), that would be quite some range on that ComBadge signal to still be able to reach the Enterprise across the Delta Rana star system.