In casual conversation I've been noticing this more and more in my own speaking as well as others. The subject will be missing from the beginning of the sentence and instead it's inferred as the general subject in the context of the conversation.
Person 1 >> "Hey, when are you coming over?"
Person 2 >> "[I will] Probably be there at around 14:00."
With the content in the brackets dropped, both people understand that Person 2 is the subject of the second sentence due to context but it's never explicitly stated.
Is there a term for this? I know ellipsis is the term used for the general omission of subjects from a sentence but is there a term for specifically The subject at the start of the sentence being dropped?