Review the sentence:
Alone at the cafeteria table, Francis's burger, which was ordered with
no onions and extra pickle, was consumed.
Alone at the cafeteria table, a phrase, comes right before burger, an illogical target. If the burger is alone, who is consuming it? That person is the logical target for the phrase, but notice that he is not in the sentence! (Francis's, a possessive noun, functions as an adjective describing burger.)
Before you continue, review the rules for misplaced and dangling modifiers.