Our beautiful backyard tree had two large limbs removed... one probably 5-8 years ago and another about 2 years ago. The larger limb area is at least an 18 inch cut. The tree materials inside that cut iare rotting and you can pick out the "flesh". A smaller limb was cut a few years ago... now it is hollow with a family of squirrels living inside. Both times the tree service said they no longer use tar to cover the wound. The tree is very much alive, but I'm concerned about the safely and life of the tree. I also was told that there are carpenter ants living inside as well.

No, we don't use tar anymore. Didn't do anything good. Now, we make sure the cut is clean and only an inch or 2 from where the limb/branch emerges. The tree heals the living tissue with food flowing down from the uncut limb/branches. The inner, dead wood, is not healed or protected. It will eventually rot and be removed by squirrels, carpenter ants, etc. It's loss will slightly weaken the support strength of the tree trunk, but that will take many years.
As a new shoot grows, it makes a tube all the way to the end of a new root. Half of this tube is a straw, sucking nutrients from the roots as the water evaporates from the leaf. It is a physical, wooden structure. The other half is live tissue, sending manufactured food and energy from the leaves to the roots (they need food and energy, too, and are definitely not green or exposed to sunlight).
All this is in the trunk near the outside, outside of the sealed wound. If you do not disturb the seal (callous, think of it as a scab), all will be well. If you start seeing cracks radiating up or down from the healed wound, with or without gum, you should call someone.