Please, don't die on me!
She ran out on me.
In the two examples above the preposition "on" seems to indicate the speaker's physical presence in the situation, in which the particular event (expressed by the verb) is/was unfolding and directly affects/affected the speaker.
Are there any other phrasal verbs in English with the same preposition conveying the same meaning? If yes, can you, please, provide some examples?
The [Wikipedia article on phrasal verbs] (https://en.wikipedia.org/wiki/Phrasal_verb) lists "teeing off on" as a "particle-prepositional verb". I would think this would also apply to "run out on" and similar constructions. The article also says:
The terminology of phrasal verbs is inconsistent. Modern theories of syntax tend to use the term phrasal verb to denote particle verbs only; they do not view prepositional verbs as phrasal verbs. In contrast, literature in English as a second or foreign language ESL/EFL, tends to employ the term phrasal verb to encompass both prepositional and particle verbs.
The article emphasizes that phrasal verbs are non-compositional, that is, that their meaning cannot be accurately derived from the meanings of the individual words. In this regard, they are like idioms.
In the examples in the question, I do not think "on" indicates the physical presence of the person denoted by the prepositional phrase headed by "on". Indeed, neither phrase clearly indicates that "me" is physically present. Rather, "on" indicates the person (or thing) affected by phrasal verb, its object.
Other phrasal verbs with on:
One of the most common three-word phrasal verbs of this kind that I can think of right off the bat would be the expression to walk out on somebody. Here's its definition and an example from the Cambridge Dictionary:
to suddenly leave your husband, wife, or partner and end your relationship with them:
He walked out on his wife and kids.
There are probably not a lot of them in English, but another one that just crossed my mind is to freak out on somebody:
Don't freak out on me like that, dude. You scared the dickens out of me!
I don't think though that we have the right to call the entire thing a phrasal verb. They actually look more like your regular two-word phrasal verbs that are just followed by the preposition on which in this case has the meaning of directly affected by or something to that effect.
Other phrasal prepositional verbs where the preposition is "on" and the object is a person are:
walk out on somebody: https://www.oxfordlearnersdictionaries.com/definition/english/walk-out
check up on somebody: https://www.oxfordlearnersdictionaries.com/definition/english/check-up-on?q=check+up+on
