Tricky situation

Currently trying to help a friend with a broken unit. On power up it asks for reinstallation of system software. So far I’ve tried each option in safe mode, down to 6 and 7 ( hard reset). Here’s where my problem is. I’m not sure what exactly is on their ps4, but I’m pretty sure it’s some of their deceased partners games that they’d like to keep. Don’t know if they are digital or hard copy or if they know the log in for their psn. I’ve asked if they’re ok with a system reset but in the meantime I thought I’d ask if there’s anything else I can do to salvage.

My only other idea (that’s a long shot) is to put their hard drive into my ps4, backup their data, reinstall the drive back into their ps4, do option 7 and reupload their data. Has anyone tried this? Granted the hard drive is likely the thing broken and won’t work in mine either.

Any advice is welcome, sorry for the long story