If you know how to handle a sewing machine .. and your existing jib fabric and the jib's overall integrity is in reasonably good shape .. and you are on a budget that is well below the cost of a new sail if there is an alternative ... Then it is possible to restore a lot (but not all) of the performance by cutting the threads holding luff tape to the sail (except right at the head), removing the luff tape (except right at the head), cutting the sail's luff fabric to a straight line between the head and tack, and then re-sewing the luff tape back on. Because all the sewing is right at the fabric edge (along the luff) and it is necessary to only sew through 3-4 layers of sail cloth, even a standard home machine will work. But you or others must have some experience sewing and with heavier fabrics. Zig-Zag feature is a must.
If this is of "I do want to do it" interest to you, I can give you more details of my experience and steer you towards some reference material. For a good introduction about the process, take a look at this video from Sailrite. In this instance, the topic is converting a hank-on jib to roller furling. But the process would be much the same for the luff surgery.
http://www.sailrite.com/Luff-Tape-Conversion-Kit-Video-Instructions.
I have done the luff surgery to two headsails and both performed markedly better. The tell-tales streamed correctly at quite a few more degrees into the wind than before. Not as good as a new sail of course. But for say $40 in materials vs the $'s for a new sail, and me not really needing new sail performance, the cost-benefit ratio favored the DIY approach.