Communicating with submarines is actually a nightmare. The saltwater ruins most radio communications, so you have no chance to receive GPS signals, which are pretty weak even on the surface.
One thing the military does/did to communicate with subs is use low-bandwidth text-only very low frequency radio, but you need colossal transmitters and there's no way the mother ship carries one. Hydrophones are also an option, and IIRC NATO even has a working sound-based modem to transmit digital signals to subs, but not sure if that has spread in the civilian market.
Military submarines also have a towed communications buoy that they can use to communicate with satellites. But that thing is connected to the submersible via a cable.
The important issue with VLF radio in this case is that what we need is sub->ship communication. VLF relies on massive antenna, often ground based to (very slowly) send message to subs. My understanding is that for comms the other way, the sub needs to raise an antenna above the surface (then possibly doing laser comms to a satellite so that no radio emissions give away sub locations).
Because there is active search and rescue happening, a much lower tech solution is to use dye. But even that presumes a canister on the outside that can be activated from the inside and which will survive the depths of the dive. In retrospect perhaps something that does that automatically if not disarmed after a certain amount of time.
I'd think some kind of (1-way only, obviously), comms system could involve things attached to the exterior that are deployed by bluetooth or something, and float to the surface regularly.
e.g. every 2 hours, send up a transmitter that sends an "A-OK" on X Khz for at least Y minutes. If you get a bunch at once, or don't get any for a while, or get the "Something wrong" on Y Khz transmitter, you know something's gone awry.
If the sub had imploded, it is likely that the implosion may have been detected by various naval assets. I don't think that SOSUS is still active but there is very likely something similar with enough sensitivity to detect this somewhere in the ocean. The question would be if classification etc would allow speedy relay of that information to the search teams etc. Granted, not much to search for if there was an implosion.