iPhone 6 plus stuck in DFU mode with black screen, not booting up.

Hi everyone, my mom’s iphone 6 plus suddenly went into the black screen of death yesterday out of nowhere. So I tried to hard reset it (power+home button), and that didn’t work at all. Then I tried plugging it into itunes and there it said it was in recovery mode and I had to restore it. So at least the battery is working. However, the issue is that she hasn’t done any backups that she is aware of so she’ll lose all her data, so this is a last resort. I also tried some iphone repair programs, and found out it was stuck in DFU mode (which should mean hard resetting should break it out, right?) , and I don’t want to pay the premium price when I’m not even sure if they will work.

At the very least, is there a way to recover her data? (More so her contacts)

Any ideas on what I should do?