Word for "someone with no responsibilities assigned to them"?

carefree

ADJECTIVE
Free from anxiety or responsibility.
‘the carefree days of summer’ Lexico

carefreeness

The trait of being without worry or responsibility vocabulary.com

But for most of us carefree living is taking no responsibilities and an escape from the world itself. ref.

Childhood is idealized as a carefree period—no responsibilities, no worries about calories. ref.

She had been eighteen, no age at all really, but though they had both been delighted at the thought of parenthood, carefreeness had flown out the window. ref.

You could refer to a carefree state/existence, or the state/condition of being carefree if that works better than carefreeness.

For completeness, a very specific term in government is: minister without portfolio.

Most government ministers have responsibility for a government ministry or department or other office (known as their ‘portfolio’).  But a politician can be given a ministerial salary and participation in cabinet meetings and decisions without that specific responsibility, by appointing them minister without portfolio.  This may be because they hold a non-government position (such as party chairman), or have an area of responsibility not aligned with the existing structures, or simply because the head of government values their participation at that level.

Floater

As in, somebody within an organization who does not have a fixed assignment. Rather, their skills are deployed as and where they are needed (e.g. paraprofessional aides who move between classrooms).

Unaccountable 2. (of a person, organization, or institution) not required or expected to justify actions or decisions; not responsible for results or consequences.

"there are enormous risks in leaving such agencies uncontrolled and unaccountable"

(definition from Google)

Unburdened, Unencumbered or unfettered first came to mind, but I feel like these words imply a being released from some obligation.

Thank you for the interesting question!