The participle is a form of verb used in forming complex tense forms or adjectives, adverbs, etc. E.g., working, talking, talked, gone, etc. Present participles end in -ing, while past ones end in -ed, -t, -en, etc.
A dangling modifier is a participle in an absolute clause that may appear elsewhere in the sentence from the subject it modifies. Also, in some cases the subject it modifies may not appear on the sentence at all. The dangling modifier is one of the most difficult constructs in language, often leading to confusion and rewrite.
Having turned the corner, the house came into view.
In this sentence, having is the dangling participle and having turned the corner is the dangling modifier. Here, the subject modified by having turned the corner is not the house. It is only the object. Where is the subject?
Having turned the corner, we saw the house.
We is the actual subject which was omitted in the previous example.
Perfectionists argue that this is a wrong thing to do, since the subject we is not appearing in the sentence, and there is a possibility for misunderstanding that having turned the corner refers to the house, which didn’t and couldn’t turn any corners.
However, in cases of no confusion as to the meaning, it is perfectly acceptable to write such sentences.
Finding good solution to the problem was difficult (for us).
Stricken by malaria, it was good to stick to bed (for me, more often colloquial).
He found Sarah, walking across the street toward the department store.
The last sentence above needs some more clarification. The phrase, walking across the street refers to Sarah, and not he. If it was he who walked across the street, then the sentence should be rephrased to:
Walking across the street, he found Sarah moving toward the department store.
He was walking across the street and Sarah was moving toward the department store.
Walking across the street toward the department store, he found Sarah.
What Sarah was doing is not specified in the sentence.
You can also write:
He, walking across the street, found Sarah.
But the dangling modifiers in the following sentences obviously need to be rewritten.
Having finished studies, the TV was switched on.
Here the absolute phrase having finished studies refers to TV, which didn’t do any studies. And it is a ridiculous sentence, hence. Rewrite to:
Having finished studies, -somebody- switched on the TV.
Somebody must have finished her studies and switched the TV on. Substitute if you know who she is.
The examination was a failure, having watched TV the day before.
Another ridiculous usage. The examination didn’t watch TV the day before. Rewrite to:
The examination was a failure to me, having watched TV the day before.
Remember the rule of thumb: modifier appears right next to or right before the subject it modifies. So, in the above example, the modifier is for me, not for the examination. This sentence may still be under scrutiny, since some people might argue that the true subject is the examination and not me, which is the object. But the subject modified by the dangling modifier is me. So it is perfectly acceptable.
Some acceptable and still scrutinized (for perfection) situations:
To get higher pass percentage, the examination was repeated.
Without knowing the route, it took time to find the address.
These sentences are acceptable to specific situations such as in spoken discourse, though seem to lack something of importance. That something is the subject, which should have been there for the dangling modifier to modify. But the subjects, since are obvious, may be omitted without much confusion.