Hi,
Regarding unexpectedness, I find come across and run into
do have some similarity. Both can be used with either something or somebody. For
examples:
1a. I came across an
old building.
1b. I came across an
old diary in her desk
1c. I came across this
problem.
1d. I ran into some trouble.
1e. He ran into
criticism after remarks he made in a television interview.
2a. I had come across so many foreigners who
have told me tales of the wonders of their own land.
2b. I've never come across
anyone quite like her before.
2c. I came across / ran into a herd of sheep.
2d. I came across / ran into an old friend of mine.
In short, I'm still at loss for the exact rules that dictate the difference between the two phrasal verbs. Nevertheless, I sense that people don't use run into with either someone they meet the first time or insentient (physical) objects.
By the way, somehow I feel come across does not fit well with either 1d or 1e, but I cannot explain why.