1. Despite Tiny being innocent, everybody thought that she was the culprit.
2. Despite being innocent, everyone thought Tina was the culprit.
Thanks.
When a subject is not present in a nonfinite or verbless clause, the normal
ATTACHMENT RULE for identifying the subject is that it is assumed to be
identical in reference to the subject of the superordinate clause.
The OP's second sentence is about Tina's (and not everyone's) innocence. In the participle clause, the writer obviously means and the reader obviously assumes Tina to be the implied subject. In the matrix clause (the part after the comma), however, the overt subject is "everyone". There is no match in reference between the two subjects, which results in a
bad sentence.
The problem with sentence 2 is not ambiguity but the breach of attachment rule. Dangling participle.
The attachment rule does not apply, or at least is relaxed, in certain cases. They do not concern sentence 2; even so, you might be interested.
1. The clause is a
style disjunct, in which case the implied subject
is the subject of the implied clause of speaking, normally I:
To be honest, you have caused us some inconvenience.
2. The implied subject is the whole of the matrix clause:
I'll help if necessary.
3. If the implied subject is an indefinite pronoun or prop it:
Being Christmas, the shops are closed.
4. In formal scientific writing, the construction has become institutionalized
where the implied subject is to be identified with the I, we, and you of the
writer:
When treating patients with language retardation and deviation of
language development, the therapy consists, in part, of discussions of
the patient's problems with parents and teachers, with subsequent
language teaching carried out by them.
Quirk et al., 1985
