I own a ranch style home with a daylight basement. There has been some sagging in the floors upstairs that seems to be getting worse over the years. In the basement there is a 10 foot section of the main wall removed to allow heat from the wood stove to circulate and open up the space. The sagging of the floor is within that area. So I had a contractor come and check it out. He cut away a section of drywall under the main beam and we found that is not even a beam, but a bunch of 2 x 8 (just guessing)boards probably nailed together. One board was cracked right were he cut the drywall and I am sure there are more failing spots we have not seen yet. I am really scared of what else we will find.
I know we have to replace this part of the main support of the house by jacking up the floors and putting an actual beam in. My question is how did this pass inspection when the house was built? Or was this common practice and allowed in 1978? Will the rest of the house be okay?

This was a common practice with a lot builders back in the day. I believe the codes have changed enough so today's builders wouldn't do this. If you have other areas in your house with long spans they probably have the same situation.

Might have been done after the Certificate of Occupancy Inspection (COI). Not uncommon for people to want something done that isn't code, wait for the COI and then go back and change things. You'll need to set up some temporary supports under the floor, pull out the damaged beam and then rebuild.