When short sighted people get old and they become long-sighted, does it make the!

No its a total myth. Having been short sighted all my life now I'm becoming long sighted my short sight isn't better at all. What is true is that I can take my glasss off to help with my long sight although as I have astigmatism as well this isnt' as useful as it might be.

No. Let me explain what is going on by introducing some technical terms.
myopia - short sighted (near sighted in the USA)
hyperopia - long sighted (far sighted in the USA)
presbyopia - what happens to older eyes.

If you totally relax the muscles in your eye, then your eye focuses for distance. There are muscles in your eye that squeeze the lens of your eye to change to focus to be closer. This is called accomodation.

In someone who is myopic, when those muscles are relaxed and their lens should be focused for distance, because the lens is not the right shape, the lens is actually focused closer. This is myopia. The more myopic, the closer the focus is when the muscles around the lens are relaxed. By contracting the muscles (accomodation), the lens can be made to focus even clsoer . For example, I am myopic (short-sighted), and without my glasses the furthest I can focus is two-thirds of a meter. I can accomodate and look at things closer than that, but anything further than 2/3 meter is blurry.

If someone is hyperopic, when the muscles are relaxed, their lens is focused beyond infinite distance. Through accomodation, they can make their lens focus closer. Many people who are slightly hyperopic don't need glasses when they are younger because they can accomodate. (extreme hyperopia is a problem because when you accomodate, your eyes naturally turn inward, making somone with extreme hyperopia appear cross-eyed.)

As people age, the lens becomes less flexible. It is harder for the muscles to accomodate and bend the lens to focus closer. This is presbyopia. The fix for this is reading glasses, which functionally make someone myopic, so when the muscles around the lens are relaxed, the focus is close rather than far. If you were to contract those muscles and accomodate while wearing reading glasse, you could focus closer, but you cannot make your eyes see further.

If someone has normal eyesight, when they age, they become presbyopic. They need reading glasses to focus close because they can no longer accomodate. They aren't really long-sighted. Their lens focuses normally for distance; their lens just can't bend enough to focus up close.

If someone is hyperopic (far-sighted) to begin with, they are accomodating a little to see things far and are accomodating a lot to see things close. As they age, they can't keep this up, so they first need reading glasses to see close and soon they will nedd bifocals because even the small amount of accomodation to see far away is not possible.

If someone is myopic (short-sighted) to being with, as they age, they won't be able to accomodate as much. But if they take off their glasses, their natual maximum focus is close (the definition of myopia), so they won't need to accomodate much to read something close.

So, to summarize, as someone gets older, they can focus on things in the distance as well (or as badly) as they used to, but they lose the ability to make their eyes focus close up.

As people age, there is another change in the eye. In the back of the eye is the retina, which is a sheet of nerve endings that detect light. This is what the lens is focusing the image onto. (The retina is like the film in the camera, or to use a more modern comparison, the retina is like the image sensor in the camera.) With age, the retina loses senstivity, so even if the lens is focusing everything correctly, the retina may not be picking everything up. This is usually experienced as nigh-blindness. Older people have a harder time seeing when the light is dim.

as you grow older all eyes become more towards needing reading glasses (long sighted) which means if you are currently short sighted as you get older your vision will start to get better and correct out.

Yes it does. That's why many doctors don't recommend laser treatments for short-sighted people.