An entity which denies responsibility simply by the act of claiming they are not responsible, whereas from other logical reasonings they would take responsibility.
Similar to the term "undead," as in, not dead, but supposed to be.
Unresponsible is not responsible, but still should be.
A car company which states "we are not responsible for death caused by mechanical malfunction" renders itself unresponsible, as an automobile company should, from a moral standpoint, be held accountable for matters of safety.
However, a company that makes clothing irons and claims "we are not responsible for burns caused by using our product while still wearing clothes" would NOT be considered unresponsible from the reasoning that the corporation can not control individual behaviour of consumers.