There are multiple definitions - click on the translation that matches your context.

ansvarlighet

substantiv

partial

liability

noun

Definitions of liability

English

(usually plural: liabilities) business debts

Pension schemes face deficits when liabilities exceed the value of the funds.

English

legal responsibility for acts or omissions (=failures to act, especially when you should have)

The Ministry of Defence pays compensation wherever there is a legal liability to do so.