Can a borrowed iPhone sync data with old Apple ID?

Once there is a factory reset, all of her data is gone from the device. She has it in her iCloud account, but you can't access that from your iCloud account. You are right... it's impossible. But that's a good thing from a privacy standpoint because anything else could be in her account, such as financial info. You have to love Apple for their privacy!

You mentioned -

I then set up the phone using my own apple ID from my previous phone and used the phone fine.

When new Apple ID is signed in the previously erased device the old iCloud data . may be photos will never sync in that iPhone .

However , her iCloud data is on iCloud server, but you must not ask her Apple ID password and account credentials Security and your Apple Account - Apple Support

Keep your Apple Account secure on iPhone - Apple Support

Note : the devices will only be merged when same Apple ID and password is signed between two devices see the article to share photos Create shared albums in Photos on iPhone - Apple Support

Erasing your iPhone will remove all the data from it. It will always remove apps and data, and your Apple account. If you want to check and make sure, you can go into the settings app and check if you find your friend’s name at the top, they weren’t signed out.

I forgot to add... if you both want to share photos, AirDrop is a great option! You can pass photos back and forth, then save them to your own device.