From the allmusic.com biography of the heavy metal band Celebrity Skin (apparently unrelated to the 1998 Hole album of the same name), a recent addition to the Fellowship of the Predicative Adjunct's collection of epically dangling modifiers:
At one show in particular, ex-Germs/45 Grave drummer Don Bolles went to review the band's live performance for the L.A. Weekly newspaper and gave the band a favorable review. The following week the band went to Bolles' apartment in hopes of persuading him to join the group. When asked to join the band, Bolles' pet rat went into a spastic fit and died. Bolles took this as some sort of strange sign and joined the group cementing his spot as the band's permanent drummer.
It may seem plausible that a heavy metal band would ask a pet rat to become its drummer, but it's reasonably clear in context that it was Bolles rather than his rat who was invited to join.
The anaphor implicit in the "when asked" clause needs to skip the following sentence's subject ("pet rat") in order to connect to the name "Bolles", which is a possessive modifier of that subject. Thus this example is distantly related to an old issue about possessive antecedents for pronouns. However, I suspect that skipping the rat will be a problem even for those who (like me) are puzzled by the "possessive antecedent proscription" in the classic cases like these: