How does hallux valgus and bunion formation cause toe hammering?

Photo: you need to recognize this predictable pattern.

When the hallux begins to become incompetent, from perhaps pain, hallux rigidus, hallux limitus, bunion and in this case hallux valgus with bunion (in this case rotational instability) when this incompetence kicks in, we must find stability elsewhere. One will often, unconsciously, begin to increase the flexor tone and pressure to try and find stability since one cannot get it sufficiently from the hallux anymore.

Here you see the tenting up of the 2nd toe, from increased long flexor activity (FDL) over time.
And here is the interesting thing you will notice, over time, the 3rd toe will start the same strategy, then the 4th. We see this often. It is not set in stone, but we see it a lot.
Notice it in your clients feet. Teach them why they are getting hammer toes, flexible ones at first, and possibly rigid ones over time. Hammer toes can have many causes, this is just one.
Solution: find a way to help your client re-find better hallux and medial forefoot stability to halt the progression.