In Ma, to get a guardianship you need to have a medical letter ( a specific court form) showing that the elder is not competent.  Marge and Homer would need to be able to show why Abe is not competent and why they should make decisions about him.  The Simpsons would need to be able to explain to the court the risks and that they would be good caretakers.  Marge and Homer could go to court on an emergency basis is there was enough of a reason or on a temporary basis.  Nowadays there is a lot more paperwork  needed and there needs to be notice to both Abe and other relatives.

The Court will run people's criminal records and in Homer's case that may be an issue.  There are also further steps that would need to be taken to admit someone to a nursing home or treat with anti psychotic medicines.  Many guardianship's are uncontested but many will be fought by family members.

There is a separate action to be in charge of Abe's  money( (estate) called a conservatorship.  Both a guardianship and conservatorship have a lot of obligations including reporting to the court.