Arrange small items (such as hot pads, etc.) in shadow boxes with appropriate memorabilia with a tribute to your relative. Just a personal preference, I probably wouldn't take a family linen apart or re purpose it but a non-relatives work w no sentiment would be lovely redone in a quilt, wall hanging or whatever. At any rate, use a pigma pen (permanent) to date, approximately if not certain, your final display. I have a huge supply of quilt literature that DIL who works at L Arts has given me. I have seen a pattern incorporating vintage handkerchiefs in a quilt top. Also, seen embroidery items made into sofa pillow covers.
Another idea is arranging in a crazy patch design utilizing your own skills to make it even more of a family memento, signing with the date and your name in embroidery on a quilt top or wall hanging. They don't have to be large, I made embroidered squares with sashes and borders from block kits that were vertical which could be used on the wall or on a table. History tells us cotton can last in excess of 200 yrs. Kudos to you for keeping textile objects a family treasure.