Question: I’m specifically thinking about emails I receive all day where someone will write:

> 
> Haven’t seen it yet. Will respond when received.
> 
> 
> 

If it were spoken, we would certainly hear:

> 
> I haven’t seen it yet. I will respond when I receive it.
> 
> 
> 

It’s mostly the dropping of *I* that I wonder about. Is there a name for this phenomenon?

Answer: 
It's not just pronouns that are getting dropped. It's whole chunks of sentences.

> 
> Will respond when received.
> 
> 
> 

lacks not just its subject *I*, but also the subject *it* and the auxiliary verb *is* from *when received*. This is the written version of **Conversational Deletion**, a very common practice in speech, discussed [here](https://english.stackexchange.com/a/66994/15299).
The dropping of *I* (and other subject pronouns) in English is called “diary drop”, after one of the contexts in which it is most common.

It is distinct from pro-drop (mentioned by @BillFranke), in Italian and other “null subject languages”, in that it cannot occur, for instance, in subordinate clauses:

> 
> Think (that) I have understood
> 
> 
> *\** Think (that) have understood
> 
> 
> Credo che ho capito [word-for-word translation of starred sentence]
> 
> 
>