My Dad got this too,he is also in NH,must admit I can't quite see the logic but that's nothing new.He was also paid £2000.00 bereavment payment when my mother died,no application was made,only contact was to report her death to DWP.As I said my Mom is a NH (and also a tax payer). The system knows that as she gets the £100 payment and not the full amount. She didn't apply for it so cannot be accused of abusing it and therefore that accusation of yours is unfounded.
Izzy has given you some links to read. I suggest you do just that.