I have a 25 x 50 table runner. There is a good size piece of the fabric I used for one of the borders. Ideally, I would like to put that on the back, but I don't think there is enough. The piece I have is 39 x 44. Is that enough to cut off some from the width and add it to the length?
Yes.
If you cut one piece 25 1/2 X44 you will have a strip 13 1/2 ' X44 left over. Cut that left over in half, and you will have 2 pieces 13 1/2 "X 22". Sew the 2 13 1/2" pieces together and you should have something about 26 1/2" X22". Cut that to 25 !/2" X22. You can attach that to your first piece that was 24 1/2"X 44 and you would have a strip long enough for the backing. To make the backing look nicer, I would center the pieced section in the middle by cutting the long strip (25 1/2" X44 in half and then piece the 25 1/2 " pieced strip in the middle. Your backing will be divided into thirds. Center the middle of the pieced strip in the middle and cut to match the front.
I have a REALLY long scrap, but it isn't very wide. It's 12 3/4 x 110 inches.
For this one cut in half, sew the long edges together. You will get a piece 25 X 54 1/2. That should work if you didn't start with the 25" width being the finished width. Just cut off each end ( about 2 1/4") to center the seam in the middle and have the correct length.
You didn't ask but I figure you might need some fabric for the binding. You will need about 160 inches. That will be about 4 strip 40-44 inch width of fabric. If you make you binding 2 1/2 inches wide, you will need 10 inches of 44 inch width fabric.
Remember to cut off selveges before measuring the width of your fabric.