A person deriving unearned benefits by being attached to another is riding on his or her coat tails. This expression derives from the long tails on men’s old-fashioned coats.
A person clinging to another’s apron strings is excessively dependent on him or her, like a smalll child hanging on to its mother’s clothing.
These two expressions are often mistakenly blended. The result is statements such as ”she hoped to succeed by clinging to her boss’s coat strings” and “he is still clinging to his mother’s coat strings.” Some coats have strings, but “coat strings” is not standard usage in either of these sorts of expressions.