I’m interested in setting a story I’m brainstorming in America during the Industrial Revolution, but first I want to know something. If a teenager and her maybe ten year old sister became orphans and they had no relatives, what would happen to them? Would they go to an orphanage?
Industrial Revolution is a broad, sweeping term. There’s a big difference between urban, small town and rural settings and the exact time period would also play a huge role.
Nonetheless, in pre-modern eras, a teenager might be deemed grown up enough to raise the younger sibling on her own. If not, I doubt any orphanage would take in the teenager, so the children would be separated.
If keeping the siblings together is important to your story, perhaps someone from the community or church steps in to give the kids a home. Maybe even in exchange for work , either housekeeping or in a business.
As Dichotomy said, it really depends on the location, exact time, etc. but a teenager is as good as being an adult for the era, most places. And 10 is actually old enough to work in a factory as well, so they’d both be expected to get jobs or go to work houses, more than likely.