Can I get audio output from TV(/soundbar) when Bluetooth headphones disconnected?

[SleepingInsomniac]

I'd like to have my TV set up in such a way that I can connect bluetooth headphones to it, but whenever they're not connected, it would default to outputting audio via the built-in speakers or a soundbar or whatever. (As opposed to me physically connecting and disconnecting a bluetooth transmitter to/from the TV every time I wanted to switch between outputs)

Ideally what I'd like is a relatively cheap (<£50 GBP, preferably) soundbar with a bluetooth transmitter (not just receiver, as seems to be pretty common), that would default to outputting through the soundbar itself when bluetooth headphones aren't connected. If anyone knows of anything like that, that'd be great.

Alternative suggestions are also welcome.

Is there anyway to do this?

 

[americanaudiophile]

A bluetooth transmitter would not have to be disconnected from the TV when you don't want to use it. The optical audio out of any TV is fixed in volume and works whether the TV speakers are on or not. You turn the TV volume down when you want to use the headphones and up when you don't or you could have both at the same time with different volumes for each.
How you would add a soundbar would depend on the connections that the TV and soundbar offer.