This sweater of Jim's falls in that category. It's a lovely 100% wool hand knit that I made for him in 1991. This past week the right elbow wore through.
Two years ago I reknit the bottom ribbing to tighten it up, and also knit new cuffs for the sleeves. That was possible because I still had a wee bit of yarn from the original project. The cuffs used all of that.
So when I wanted to fix the right elbow I looked around for something suitable. This dark brown was maybe the best I could do.
I picked up 17 stitches quite a few rows beneath the hole and started knitting. At the beginning and end of every knit row I picked up one leg of the stitch on the sleeve and knit it with the first or last stitch on the patch row. That meant the bottom and the sides of the patch were part of the sweater now.
When I got to the top, far enough above the hole I did a sort of Kitchener stitch to finish it off. I cut a fairly long tail of yarn and threaded it though a yarn needle--the needle with a blunt point used to sew knitted garments together by hand. First it went purl wise through the first stitch on the patch needle. Then I threaded it behind the loop of the sleeve stitch, brought it back to the first stitch and inserted it knit wise, sliding that first stitch off the needle. This was repeated with each stitch on the patch needle: Purl wise in the patch, from right to left behind the loop of the sleeve stitch, then knit wise through the patch stitch. It makes it look as if the patch is knitted right back into the sleeve at the top.
This sweater has been in the category of work clothes, not dress clothes, for some time now. I'm just sorry I couldn't find a better match, colour wise, but this will do fine as a remedy for the time being.