Can these floor boards be saved?
Since the floor is so thick, that has a lot going for it. Since it sounds like the holes are over a large area in a part of a room, that is not so good. Not knowing how bad the wood boring insects affected the wood, it will be hard to be definitive with an answer. The safest solution without knowing more about the floor, would be to replace the floor, since the one small section included in the picture does not represent how much damage the floor actually has.
If there was a way to determine the full extent of the damage and found it repairable, it could be done in 2 ways.


The first picture is the simplest, but it will leave cracks where things can still fall through.
After all the cutting out of all the damaged material is done, I would have a pest control company look over the bug damage to see if they are still active, and let them act accordingly, then make the repairs.