I checked Thesaurus for incident, but the synonyms are "milder" version of the word.
Is there one that has the connotation of being bizarre? (e.g. a pet hangs itself on a tree).
After hearing about the [...], she almost went crazy.
I'm not sure that a neighbor killing a cat is such a bizarre thing (alas). A pet being killed by a meteorite, I would call bizarre.
An often-used synonym for bizarre is freak, as in freak incident. This means it is an incident that nobody expected to happen, that seemed very very unlikely or is the result of many unexpected things all coming together.
Another possibility, with a different connotation, is an act of god. This is used to describe something that happens outside anybody's responsibility. It is often used in insurance policies and the like to indicate the kind of incidents that one can not reasonably expect to prepare oneself for. These usually include things like earthquakes, volcanic eruptions, etc.
Note that act of god does not really bear any religious connotation, notwithstanding the god part.