Can an informant caregiver get POA after the death of a loved one or does being an informant give you POA?

Sorry, I don't understand what you mean by informant?

I'm going to guess that the person who had POA has passed away and now the person they were looking after has no one else? You need to see the POA documents, sometimes there is an alternate person named if the first person can not serve any more. If there is no alternate named the person who needs someone to act for them can draw up and appoint a new POA if they still are mentally competent.

POA ends with the death of the principal- no one can have POA. After death it is a matter for the executor named in the will and/or appointed by a judge in a court of law.