I think your staggered-joint idea is a good one. From the look of it you'll have a solid enough base to get another decade or two from that tail.
I'd cut back just enough to get solid wood at the center, then notch the sides back to wherever you can comfortably fit the saw. Something like so:
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Fasten the cedar or pressure-treated repair pieces with good exterior-grade adhesive and trim screws. (You can even fasten the most conspicuous side from the inside to keep the surface smooth.) Caulk against the wall, and stain or paint to seal the new wood.
I think I have mentioned it on the site before but I used to specialize in buying termite houses. In Arizona they are quite common, in the Midwest not so much.
I disagree with Keshlam in saying it is too much trouble, and walk away. I think the sensible thing to do is figure out what you want out of the house and what it will cost to fix it.
If you want to buy a house an just move in and live there and touch it very little then you shouldn't buy a house with termite damage. In actuality your house choices are going to be extremely limited.
If you would like to update a house and make small living changes, this could be the perfect house for you. In the flipping business we know it is much more cost effective to gut something then work around everything.
How do you assess termite damage. You do it yourself. That is fine that you had someone help. I would go around the house with a fine tooth comb and document any kind of wood damage, any kind of paint damage, any sagging or structural issues. Everything should be attributed to termites.
So the main assessment is centered around if the termite damage is on the outside of the house - most houses are like this or is it pervasive through the whole house. You really need to spend a good deal of time in the attic (trusses, floor beams, and plywood sheathing under roofing) and in the basement looking at the structure. Framing and cosmetic things on the outside of the house can be fixed easily.
The next step is to get a quote from someone that can come in and fix everything on the outside, drywall and simple framing. Double that quote and take that off the price of the house. Remember that home owner has to now disclose this damage to all new people who look at the house. Mention this to them and use it as a negotiation technique.
Really if you aren't looking to make money off the house you need to figure out if you want to manage the fixing of all this stuff to make it look exactly how you want or do you want something that is more move in ready. There is NOTHING wrong with buying a house with heavy termite damage, you just need to set your expectation and it would probably be cheaper and faster if you didn't live in the house while the inside stuff was getting done.
Note: I mention to double your quote because I have found from experience that most termite quotes end up on average at 1.5 times original quote. Double it because you are managing it and might not be living in house for 1-3 months depending on damage. Also I should point out, be fully aware of any asbestos potential (think flooring, popcorn ceiling and ductwork). This is an important caveat because when you start opening stuff to fix termite damage this is really the only thing that can prove to be costly real quick.
Best Answer
No, the "by the book" way is to remove the beam all the way back to where there is no damage and replace it. I doubt this is termite damage it is likely dry rot from a roof leak. If your roof is NOT leaking then the dry rot will not continue to happen and in fact if the roof was ever redone it could have been leaking before and they just were lazy and decided 1 beam wouldn't be a problem if they even noticed it.
This is not uncommon in roofs.
In your case if the roof is not leaking you can safely ignore it until the roof wears out and needs to be replaced. Then once they tear off all the shingles you can have them remove the boards from that section and then remove and replace the beam once the roof joists are exposed. If it is just this one beam it's still safe since the roof isn't weight bearing (unless you live in an area where it snows heavily) but if you can get inside the attic and look at all the beams that would be good.