First one I can remember was from Mary, a former college basketball player. She contacted me several years after she graduated, said a former teammate had died and she told family she would see about acquiring pictures of her late former teammate in action. I searched my archives, found a few pictures of Mary's former teammate, put them on my site (with a reasonable price), told Mary about it, and she ordered nothing. I could only assume she had been angling for free pictures all along.
A few weeks ago a college employee and Facebook friend asked via Facebook message if I had pictures of the former football coach there, who died two years ago. I had just finished building a gallery of coach pictures and sent her a link to ten of the coach she was interested in. She wrote back asking for a discount. I declined to provide one. And she bought nothing. As it happens, she was asking on behalf of the coach's widow, who wanted to make a collage with pictures of her late husband to hang in the football locker room. She said the widow cried, but I'm not sure if it was after seeing the pictures, or after I declined to give a discount. Anyway, no one ordered anything.
...surreptitious implies deceit. I don't see deceit here at all. These aren't typical photo buyers. I can hazard a guess your marketing plan is not orientated around the recently deceased. These are people in grief. They don't understand the "process." They asked you if you had photos of people that had passed away. You said you did: and you named a price. That price was too high: so they walked away. There is nothing surreptitious here. This is just the free market in action.
You can run your business how you want. I would have sent them the photos. For free. No obligation. I may have even done the collage for free and sent them a print. Life's too short to worry about $5.99. I make my money elsewhere. Do you want to be remembered as the photographer who made the the wife of the beloved coach of the local high school cry? Its a shame that this football locker room doesn't have a framed photo of this coach, kindly donated by Rod Cannon Photography, proud supporter of football at this school.
If you are "suspicious" that she wants free photos then tell her upfront that there will be a cost to search your archives, and bill her before you search. I think Scott's suggestion is very good.
My event print sales are going down as well. I charge a higher fee upfront now, and don't cover events that I either don't enjoy, or look to be unprofitable. The market has moved on. You need to be talking to your client base: find out why they are not buying, and figure out ways to meet their needs. And if you can't change your business model to accommodate their needs (and make a profit) then walk away and find a new way to make money in photography.