The lady had already received a call from her husband to say that her cat had died so it certainly wasn't a discovery or a surprise when she got home. If there had been no telephone call, she had simply left work and driven home at the end of the day and walked in the front door of her house and then saw her cat lying dead on the floor, you would say "She got home to find her cat dead".
To use it to mean purpose, you could say something like "I am going to home to find my keys. I can't find them on my desk". "I'm going to Greece to find my one true love". In this context, it actually means "to search for and hopefully to find".
Student or Learner