I'm sure I should have asked this sooner, as this was something our cat was doing for months, although we didn't pay attention to this until vomit started to appear in our house.
Long story short, we give two of our cats (Chilli and Luna) some treats once every two days. We limit the amount of treats to around 3-6. Chilli breaks them down with her teeth as usual, however Luna mostly doesn't. We'd often find vomit behind sofa or in the corridor. We concluded that the vomit appearing in our house belongs to Luna. This doesn't happen often, but we are pretty sure it would be due to these treats as we caught her vomit a few times, hours after swallowing the treats. Also, she seems fine other than the occasional vomiting.
Is there a way to teach my cat (Luna) to break down her treats before she eats them? I'm not looking forward to refraining from giving her treats as we'd like to continue to give rewards for activities. Also, the treats in question are about as small as the 'dreamies'. Would giving them bigger treats be a good alternative?