Death of a principal terminates every power of attorney (some curative statutes allow a power of attorney to have effect until the death is discovered by the agent to make it safer for people to rely upon agents). Obviously, dead people can't act as agents, and less obviously, a person's estate does not as a default matter assume a dead person's agency responsibilities. At common law, the disability of the principal also terminated an agency automatically, unless it was a "durable power of attorney."
A Chapter 7 bankruptcy immediately vests all property and economic legal rights of the filing debtor in the bankruptcy trustee, and often principal-agent relationships are not assignable. An appointment of a receiver can often have the same effect.
Your real question seems to be when a successor agent may take over from a primary agent who is failing to carry out the duties of the position or breaching a fiduciary duty to the principal,wouldn't be a termination of an agency relationship by operation of law, rather than a change in the legal status of the agent such as death or bankruptcy or dissolution of an agent that is an entity, which normally would be a termination of an agency relationship by operation of law.
Certainly, failure to pay debts when it is possible to do so and/or failure to carry out a court-ordered settlement would be grounds to have a court remove an agent for breach of fiduciary duty and failure to act. The hard question is whether you could have the authority to take over without court action. This depends to some extent upon the language of the power-of-attorney instrument. I normally draft mine so that "failure to act" is one of the conditions that triggers the authority of a successor agent, and the kind of conduct you describe would constitute failing to act, but not all documents are so clear. Also, it isn't entirely clear that a "failure to act" provision as opposed to a removal of agent clause applies when the agent has taken action in the past (as opposed to never doing anything).
It is also often unclear how long "failure to act" must last (the default is a reasonable time which is often taken to be a month but can be facts and circumstances dependent based on the harm due to inaction) and whether there is any duty before taking over to urge the first agent to do something and then to not get an adequate response.
All this matters because the main use of a power-of-attorney is to secure third party reliance on it and acceptance of it and this often won't happen unless the transfer of authority is very clear. The conservative approach which may be necessary would be to go to court and seek a declaration that the first agent is failing to act so that the successor may act, on an emergency basis, after first trying to get the first agent to resign voluntarily in writing.
