Friday was coming home from work and noticed the rear cassette was not moving to the smaller cogs.
Initially though it was a cable stuck somewhere or needing a tune up. Got home and while trying to tune up the cable snapped inside the shifter.
It was surviving on few threads and probably was stuck itself and not shifting to the smaller cog.

I think I had around 3.5k to 4k miles on it.
Is that around the expected life? I've never lubed or anything inside the shifter body.

When these reports like you posted started coming out I started lubing the cables inside the cable holder in the shifters periodically with Tri-flow, the one with the long needle dispenser and know I get much more that the life than your post (sorry I have too many to keep accurate records) but as you no doubt know that greatly depends on the shifter, housing, cable quality and environmental factors, etc,. The only problem I have encountered is when a few strains broke loose from the cable in a Shimano shifter long after initial break in period and I looked and found the cause of the stretch. I agree the reason you could not get to the small cog, a big clue, was a few strands broken loose hanging up the cable not allowing a full return to slack cable.

Periodically and any time there is s sudden change in shifting, check for fraying cables. Hopefully you did not undergo too much pain getting the broken cable head out of the shifters, sometimes it is a long and tough job; much easier if you catch it before it breaks off.
The tight curves required for under-tape cable runs makes fraying a much more frequent occurrence so vigilance is key to avoiding unpleasant surprises. We have seen posts on this forum of folks getting far less mileage than you, but of course it is number of shifts not mileage which is the key metric.

Somewhere in Shimano's many published guidelines has been the maintenance "need" to replace shift cables periodically. I don't recall the frequency but 6 months comes to mind. Which I remember thing was crazy, unless you are mega mileage and/or just really hard on your cables.

We have a couple of customers who have told us to replace their cables whenever they have their bike tuned (which is generally once or twice a year for these riders). Andy (who also has fished out a broken off cable head from his shifters, but being an Ergo guy it was easy)

Thank you for feedback.
Removing the head was not that hard since there the 105 5800 has some covers on the bottom side of the shifter body as well as where the cable goes to the housing.
After removing the cable head I shifted many times and removed any pieces of cable left there.
I thought I did it diligently, but today when riding to work after some 2 miles, click to move to smaller cog and ... nothing?
Stopped and pulled the cable manually and all starting working again.

Will open it tonight and see (try) if some small piece is lost there....

I don't see any mention of replacing the cable housing above. It's a good idea to replace that when you R&R the cable. Make sure the housing is cut square and doesn't have any sharp edges, and if the housing isn't lined, grease the cable as you install it.