Does the dangling modifier thing apply?

I have a persistent question concerning grammar that I would really like your help on. It has been nagging me for a long time.

So, as we all know, if you start a sentence with -ing, the first word of the following phrase/clause has to be the subject that the -ing is modifying.

A: Feeling dejected, Tom left the pub. Tom--the one feeling dejected.

B: Swimming across the ocean, the old man pushes forward with every ounce of strength he has got. The old man--the one swimming across ocean.

However, when -ing occurs in mid sentence and at the start of a clause/phrase, does the "dangling modifier" rule still apply?

C. Pancreatic cancer is common among the elderly, necessitating the need for screening in the specific population.

Here, pancreatic cancer itself does not necessitate screening - it is the whole situation (P cancer common among the elderly) that necessitates the screening. But I read sentences like that all the time.

D. The company will experience slow growth, driving the need to seek for new income sources.

Here, the company itself does not drive the need -again, it is the situation ( slow growth ) that is "driving the need".

So, I would like to know if :

1. C/D are correct or they are plain wrong.

2. the -ing occurs at the start of the phrase/clause but not the start of a sentence (i.e. C/D) - does the "dangling modifier" rule still apply?

Or starting with -ing in the second clause/phrase is a whole other thing (which means it serves more of a transitioning function and not intending to modify anything?)

The question is a tricky one, because the phenomenon you describe is common, and would, if I think back, have been objected to by my English teacher some sixty or so years ago. So far as I know, no special rule or technical term has been established to 'allow' it. There are, of course, easy ways around the structure. You can add "...for that particular age group", but why bother , if the correct meaning is apparent anyway? If we must be strict, we can describe it as being "a participle phrase in apposition to the sentence".

There is a useful passage about this in Sydney Greenbaum's Oxford English Grammar (published 1996).

Apposition ... is similar to o-ordination in that the linled items of equivalent grammatical status. The difference between them is that the linked appositives are identicalin their reference (refer to the same person or the same thing) or they overlap in their reference (one appositive in reference to the other). Typically, the units in apposition are noun phrases.

So, the participle phrase in C can be treated as a participle phrase in apposition to the sentence - that is, to all of the sentence, including the age range of the principal victims. The device is very common in the prose and verse of ancient Latin and Greek.

I think much the same can be applied to examples A, B, and D, though C is the most obvious.

Example A is not quite as obvious, but the term apposition does apply. That is, the second part repeating "Tom" is in apposition to the opening sentence and adopted its grammar, including the verb. Similarly with examples B and C. The use of apposition is important in literature, because it tightens prose (or verse), provided the readers keep all of the sentence(s) in mind as they read. The tightening often intensifies drama and emphasis, particularly in Sentence A.