I recently came across a real-life story about a woman from the 1800’s who lived an incredibly interesting and tragic life (albeit with a decent ending to it).
I’d love to write a work of fiction using some of these events, without using real names, places, etc. but I’m not sure if that’s appropriate.
She passed away in 1906 and has no direct heirs, but I know that several (very) distant relatives have written blog entries about her and there was at least one non-fiction book written telling her story.
Another relative has been working on a documentary and although it’s been in the works since 2011, it has yet to come to fruition.
Although I am planning on this book being a work of fiction, with many events changed or added, anyone familiar with her story would probably recognize it, and I wondered if that could be a problem.
Using real people is very common in historical fiction.
The fact you are asking this makes me wonder if you've done enough reading in your category yet?
You need to know your category, particularly books published within the last two years, VERY well. This is where we all thank god for libraries because this kind of massive reading would be prohibitively expensive without the library.
If you're asking because most of the historical fiction seems to be about recognizable names, and your character is not so well known, you're still ok. You can't libel the dead and sans heirs, estates, or something of value to protect, no one has standing to sue for damages.
If you're asking because someone who has written blog posts, or started a movie might have "dibs" on the story, you're ok. You don't get dibs on a subject or even a person. Copyright is only for the actual work, and copyright doesn't preclude anyone from writing about the same person or subject. It only protects the rights holder from someone taking their words (or pictures) without permission.
The other thing that raises my eyebrows is "without using real names and places." I'm not sure why you wouldn't use real names and places. If the story happens in Wichita, why would you set it in Buttonweeezerville instead?
Again, this sounds like not enough research. Which might be good news: now you have a legitimate reason to read 100 books and not feel like you're being lazy and not working!