Cotinuous without "to be"?

I'd suggest we think of it as a special case where you don't really have someone describing something to you, as much as you have a sort of non-narrator providing essentially a stage direction. "The killer enters," might be a phrase in a play's stage direction. You can see this is a special, different situation from an actual person describing the situation to an observer. It would sound odd to say it that way. We'd expect something more descriptive, like, "the killer is sneaking up."

I think it is extremely helpful for subtitles to work this way. Not only is it more efficient by using fewer words to say "Jennifer speaking" instead of "Jennifer is speaking," but it gives a different sense of the text that represents dialog from that which provides that stage direction function. Sometimes subtitles try to further the distinction by using a different font, but you also have off-camera dialog to contend with. A character on-camera can say, "Jennifer is speaking." An off-camera character could also say that, but their dialog would be italicized, I think. But if Jennifer is on-camera, but her back is to the viewer and we can hear that she is speaking but can't make it out, then there is no dialog to show and I'd want to see the subtitle simply indicate she is speaking by saying "Jennifer speaking" or "Jennifer [inaudible]" or something like that.

I have the knowledge of the use of this kind in certain announcements that read 'admissions going ' , ' repair works going ' and the like . At first they ,with their apparent lacking of the helping verbs ,hit me right in the eye but having come across the sentences of such kind particularly in advertisements or announcements , I have got used to them .

While you would not write " Jennifer speaking " on a sticky note, you would not say "Jennifer is speaking, " on the phone. Language is adaptable.

I think the present participles are just modifying the noun, like in the sentence, "All I could hear was Jennifer speaking and a dog barking." It omits the article before dog like you'd see in a headline or, as mentioned, stage directions.

I think they use short phrases rather than grammatical sentences so that the subtitles are quicker to read and the person has more time to view the picture.

(This is) Jennifer (who is) speaking.