We had these dining room chairs that have slatted backrests (so vertical wooden "bars") that are spaced further apart toward the top of the chair, and curve so they are closer together toward the seat of the chair. One time my cats were play-fighting and one of them jumped up onto the seat of the chair and was batting at the other cat (who was behind the chair) through the slats. At one point the cat on the chair got up on her hind legs and then came downward again - and she got her head in between the slats at the top, then was stuck because she went down too far. Thankfully I was like three feet away at the time, so I was able to grab her (not for a lack of scratches and hisses, she began to panic as soon as it happened) and pull her up and out. Fucking terrifying. If I hadn't happened to be there she probably would have choked to death.

I got rid of those chairs shortly after.

I'm sorry about your sister's cat, and sorry you had to be the one to find her. Freak accidents happen, and it's just awful, but at least she had a long happy life prior.