I don't really see how the person making this this (unreasonable) demand for payment can expect it be effective unless the deceased singer and the songs are named. Otherwise, most singers will presumably remain unaware of the request and carry on singing the songs they enjoy, even if - perhaps especially if - they have a particular fondness for a version that used to be sung by the now-dead singer. In fact, I can't think of a nicer way for a singer to be remembered than this.

In any case, it makes no sense at all to me to suggest that any payment is due, and if it were in the UK I'd say the appropriate response is a polite but firm refusal to pay. Even in the US, I can't imagine that there's any legal obligation to pay to perform a song that is neither composed nor arranged by the person demanding payment (or their heirs/estate).

Marje