I saw this on a website.

Problem:
The Taliban were not held in captivity for three months.

Explanation:
The full sentence was “After being held in captivity for three months, the Taliban execute a local official when their demands are not met.”

The sentence appeared at a website that tracks Islamic terror attacks.

This sentence documented an attack — by the Taliban, not ON the Taliban — that was purported to have occurred in Kunar, Afghanistan, on 22 November 2008.

The problem with the sentence is that “the Taliban” immediately follows the comma-terminated “After being held in captivity for three months” and therefore implies to the reader that the Taliban were held in captivity for three months.

I usually appreciate the use of active voice instead of passive voice, but this sentence calls for passive voice after the comma.

In other words, the correct way to leave the “After” clause in place is to say immediately after the comma WHO was executed.

Solution:
“… held in captivity for three months, a local official was executed …”