It turns out that fungus growing termites sometimes cultivate Termitomyces titanicus. This is an excellent scientific name.

CORRECTION:
I assumed they had to work like ants. Wrong! (A fruiting body would only emerge from a dead ant colony not so with these termites) Something about macrotermitinaes nuptial flights stimulates mushroom fruiting. (!) They get covered in pink spores.

And you can eat it!

Hence the species name.

The fungi farmed by ants (Leucoagaricus gongylophorus) also produces mushrooms when their colonies die out. This fungi can't survive without the ants and the ants propagate it by carrying it with them when they found new nests:

So what is the purpose of the mushrooms?

Is it just a hold-over from the days before the fungi was dependent on ants?

I've been trying to find out if you can eat the ones that grow on old ant nests.

https://sauropods.win/@futurebird/111311901058937024

@futurebird mycologist partner didn't know about the mushrooms, says thanks for the info. She says 99% of mushrooms are not seriously toxic but you don't want to get the one that is!

These are handy for the ants because they procure plant carbohydrates stripped of all the chemical defenses the plants use to stop ants eating them. Sneaky!

When the ants are gone is when nutrient levels drop which is typical mushroom forming time. It's possible they reproduce mostly asexually (via the ants) but undergo occasional sexual reproduction to shuffle the genes once in a while (some fungi do this). If you could send a mushroom to a mycologist they might be able to answer some of these questions.