A hanging participle or adjective, also known as an unattached participle or a dangling participle, is a grammatical construction in which a sentence-initial participle or adjective phrase cannot easily be construed to refer to the subject of the sentence it precedes. Such constructions are sometimes hard to understand and are considered to be grammatical errors by some.

For example, in the following sentence the participle finding is associated with the noun mangoes, but it is not mangoes that find mangoes impossible to digest:

Finding them impossible to digest, mangoes are never on his breakfast table.

In this sentence, the participle finding clearly refers to the subject of the sentence, namely John:

Finding them impossible to digest, John never eats mangoes for breakfast.

Here are some similar examples, with suggestions as to how to make them easier to comprehend (or more grammatical, on some views):

Walking to work, a dog bit him on the leg. (> Walking to work, he was bitten on the leg by a dog)

Caught redhanded, it was easy for the police to arrest him. (> Caught redhanded, he was easily arrested by the police.)

Carelessly discarding a cigarette, the forest was soon on fire around him. (> Carelessly discarding a cigarette, he was soon surrounded by burning forest.)

However, some participial constructions do not need to agree with the subject of the sentence:

Generally speaking, it is easy to to hit a sitting duck.

Owing to bad weather, the festival has been canceled.

Taking the long view, it's better not to smoke.