That's an excellent question and a totally understandable concern. I'll do my best to elaborate.
The short answer here is that we encourage the end-user to contact the original buyer of the part or tool, and for that original buyer to contact us regarding a replacement. If the original buyer is deceased, then the end-user should provide us with some form of proof of purchase so that we may correctly identify the part in question.
Here's an example:
Mayer buys a logic board and performs an install for his customer, Kyle. Mayer never tells Kyle what the order number is, only that he bought it from iFixit. Mayer dies. RIP Mayer. Years later, Kyle begins encountering an issue caused by that logic board. Kyle contacts iFixit and requests a warranty replacement.
Kyle's only proof of purchase is that he can send us photos of the logic board, and tells us, "A gentleman named Mayer purchased and installed it for me, back in February of 2018."
Solid information! We can now identify the original buyer (you) and track down the exact order it was under. At this point, we'll talk about the problem Kyle is encountering and, if a warranty replacement is possible (meaning we have at least one replacement in stock, or that Kyle didn't accidentally destroy the logic board), we'll ask for Kyle's shipping address to send a replacement to them.
Without an order to view or track across our various marketplaces we will be less able to issue a warranty replacement because we cannot confirm exactly what we are replacing. Some exceptions to our proof of purchase requirement can be made. For example, if you bought an iFixit Pro Tech Toolkit from a garage sale and don't know the original order number -- we would still gladly replace bits and various tools from this kit despite a proof of purchase not being available. We'd just like to see a photo of the kit that you have and photos of the bits you're needing replaced.
More expensive and less available parts, like logic boards, will likely be more difficult to replace without seeing exactly where it came from, and also confirming that the replacement we're sending will be compatible.
I hope this provides ample explanation about how our warranty procedure would work in cases like this. Let us know if we can clarify anything further. :)