The employee can be sued if the employee personally participated in committing a tort, or entered into a contract as an undisclosed agent of the corporation.
While this is rarely an issue for a solvent large corporation, employees are often the more desirable defendant in a thinly capitalized closely held corporation in which the wealth owner of the corporation does a lot of the work in do it yourself manner.
This could include a breach of a legal duty owed by an officer or director that ran directly to a shareholder (although most such duties run only to the corporation and not to individual shareholders and could only be enforced by the corporation or by shareholders bringing a derivative action).
An employee is not liable for breach of contract when entering into a contract as a disclosed agent of the corporation. Similarly, an employee could not be held liable purely as a consequence of a corporation's ownership of property (e.g. potentially responsible party liability under CERCLA, the Superfund law).
Fraud is a tricky area. The Janus case held that for purposes of federal securities laws, an employee or agent who knowingly drafts a false offering statement issued in the name of the company and not any employee or agent, that only the company has federal securities law liability, but the rule is the opposite in most cases for state common law fraud liability, under which both the named author of the fraudulent statement and anyone who participated in drafting it could be held liable.
An employee could also be held liable on a fraudulent transfer theory if the employee was given corporate property by the corporation when it was insolvent that was not supported by reasonably equivalent consideration.
Certain statutes also create personal liability for employees. For example. under the Internal Revenue Code a person who is responsible for writing checks withholding taxes from employees has personal liability to the U.S. government if the tax is not withheld as required by law.
Even when an employee is not liable to a third party, an employee or agent can be liable to a company for breaching a duty owed to the company (e.g. a duty not to disclose trade secrets pursuant to a non-disclosure agreement).
An employee or agent can also be responsible to a company for causing a company to be bound to an agreement because the employee or agent has "apparent authority" to do so, even though the employee or agent didn't have actual authority to do so, if the overstepping of the employee or agent's boundaries causes harm to the company.
The rules are different for government employees who have sovereign immunity for most of their acts not specifically excepted by statute unless they constitute intentional violations of civil rights for which they have no qualified immunity.
The perpetrator of the accident was one Captain Joseph Hazelwood of
the vessel. From what I understand, he was sued, even though he was a
"mid level" employee. Was it his tie to the incident that allowed him
to be sued?
He would have liability as a consequence of his own personal negligence.
Change the facts some. A janitor or plumber working for a contracting
agency in "servicing" a client negligently flipped a switch that
caused the client's building to be burned down. I would imagine that
the agency could be sued. Can that person also be sued, or is s/he too
"low level" for this?
Yes. The employee whose negligent act caused the problem could be sued.
Put another way, my understanding is that a person needs to have
"standing" in order to be a plaintiff in a case. Is it true that
someone (even if low level), similarly needs to have "standing" (or
its equivalent) to be a defendant, and if so, what constitutes such
There is no equivalent to standing for defendants. They either have liability under a theory brought by a plaintiff (which generally requires a causal connection pursuant to a breach of duty by the defendant), or one doesn't. Standing need not be shown to raise an affirmative defense.