There have been some dates but they always get put back, probably because DAB take-up has been very slow.
I think we have to look at national broadcasters and locals separately.
I can envisage the shutdown of the main FM transmitters (or conversion to DAB only if possible - I've not followed the tech on this) so no more BBC, Global Radio (LBC/Capital/Smooth etc) and a few others. Someone somewhere up the authority chain will have a cut off point, where sufficient have moved to digital in whatever form that the FM broadcast will cease, just like it did with analogue TV. I would be amazed if it happens this decade though.
However if I spin my FM scale I find lots of little local stations, some legal some illegal and it will be interesting to see what happens to those. Most also use the web but I suspect it will be many years before the FM band falls silent.
If building or buying your own mini transmitter doesn't appeal, you can always build a little FM modulator to squirt whatever you like up your FM tuner so they will never become unusable.
That's very much a tool for the collector though.