I cut off all ties from my dysfunctional family and plan never to return to their city. Am I in any way legally responsible for my mother?

What state are you in, is your mother living in? Some states do have filial responsibility laws - it can get complicated. Other posters on this site can be much more helpful, but they would need to know the state in question. Since your mother gives your sibs permission (assuming she is legally competent) there is not much you can do - could there be an issue of Medicaid lookback down the line? Is she aware of those rules? Have you told her that you will not be further involved?

From Wikipedia
This is long but surprising and interesting.

Filial responsibility laws (filial support laws, filial piety laws) are laws that impose a duty upon third parties, usually (but not always) adult children for the support of their impoverished parents or other relatives.[1] In some cases the duty is extended to other relatives. Such laws may be enforced by governmental or private entities and may be at the state or national level. While most filial responsibility laws contemplate civil enforcement, some include criminal penalties for adult children or close relatives who fail to provide for family members when challenged to do so. The key concept is impoverished, as there is no requirement that the parent be aged. For non-Western societies, the term "filial piety" has been applied to family responsibilities toward elders.

A “filial responsibility law” is not the same thing as the provision in United States federal law which requires a “lookback” of five years in the financial records of anyone applying for Medicaid to ensure that the person did not give away assets in order to qualify for Medicaid.

History

Filial support laws were an outgrowth of the Elizabethan Poor Law of 1601.

At one time, as many as 45 U.S. states had statutes obligating an adult child to care for his or her parents. Some states repealed their filial support laws after Medicaid took a greater role in providing relief to elderly patients without means. Other states did not, and a large number of filial support laws remain dormant on the books.

Generally, the media has not covered filial responsibility laws much, and there has not been the political will to see that they are enforced. As of 2012, twenty-nine states have such laws on the books, and a few states require the potential support of grandparents or even siblings.

Support required

Typically, these laws obligate adult children (or depending on the state, other family members) to pay for their indigent parents’/relatives' food, clothing, shelter and medical needs. Should the children fail to provide adequately, they allow nursing homes and government agencies to bring legal action to recover the cost of caring for the parents. Adult children can even go to jail in some states if they fail to provide filial support.

States with filial responsibility laws

Alaska, Arkansas, California, Connecticut, Delaware, Georgia, Indiana, Iowa, Kentucky, Louisiana, Maryland, Massachusetts, Mississippi, Montana, Nevada (Nevada law only addresses support of children and not support of parents. NRS Chapter 125B), New Hampshire, New Jersey, North Carolina, North Dakota, Ohio, Oregon, Pennsylvania, Rhode Island, South Dakota, Tennessee, Utah, Vermont, Virginia, West Virginia.

Source: Filial Responsibility: Can the Legal Duty to Support Our Parents Be Effectively Enforced? by Shannon Frank Edelstone, appearing in the Fall 2002 issue of the American Bar Association's Family Law Quarterly, 36 Fam. L.Q. 501 (2002). Lexic.com.[9][10]

In addition, the Commonwealth of Puerto Rico also has filial responsibility laws.

Trial case

In 2012, the media reported the case of John Pittas, whose mother had received care in a skilled nursing facility in Pennsylvania after an accident and then moved to Greece. The nursing home sued her son directly, before even trying to collect from Medicaid. A court in Pennsylvania ruled that the son must pay, according to the Pennsylvania filial responsibility law.

The footnotes are on the Wikipedia site.

I did realize that Medicaid rules are something entirely different from filial support. My purpose in talking about lookback rules to mom was to warn her that her generosity might have bad consequences for HER down the road. As in, you do realize that I'm out of here, you have to provide for your future, so be warned this might come up to bite you. Mom probably thinks that SpiritDancer will rescue her and has given no real thought to the consequences of her recklessness with money.

MACinCT

Here is another site saying that CT has a law on the books for filial support. But it doesn’t list Maine.

forbes.com/sites/northwesternmutual/2014/02/03/who-will-pay-for-moms-or-dads-nursing-home-bill-filial-support-laws-and-long-term-care/amp/

Because it's in the books doesn't mean the law is used.

Since your siblings are mooching off Mom then they are the ones responsible for her. Just walk away. Nothing you can do if Mom is not willing to stop allowing ur siblings taking advantage of her. You do not have to except a POA. Guardianship has to be filed by you so no problem there. Seems like enough people to care for Mom. Go live your own life. Call Mom when you can. Send flowers but nothing that can be sold or money. If you r asked to help, tell them they owe Mom. If u do feel you can help, pay utilities or whatever directly.