It could be they left a roof in poor shape for too long and over the years it rotted. I would take off a section to see how bad the problem is. I might mean you only have to replace the fascia. Good luck.

It’s hard to tell from the pictures, but it doesn’t look like there is flashing that goes under the shingles & extends onto the facia? Can a screwdriver go through the facia? It doesn't look that bad. Do you have soffit vents?

The detail I'm looking for is drip edge metal. I can't tell if it's there or not from the pictures.

Joesph Corlett that was the word I was looking for!

Thanks for the responses. I found a “This Old House” video and it looks like the drip edge is not installed properly. They put a trim piece between the drip edge and fascia, which then defeats the whole point of the drip edge. We need to remove that trim piece and will hopefully be ok. The shingles are al supposed to hang over the drip edge, but there’s nothing we can do about that now. We took the trim piece off one section right before a heavy rain and it was a huge improvement, no more water running down the fascia.