I don't know what is meant by dub, but I know remixes. Most of the time, those who made the original pay someone to make a remix. I believe Madonna paid a high amount for a dance remix of one of her songs by someone who's name I can't remember right now.
There is another concept, sample use. You take a piece of an old song and make a new one around it. If you use the original sample, you have to pay for it if it's commercial. For vinyls, original samples can be used. There is a good track from a couple years ago that was only released on vinyl for dj's and for a certain radio I listen too. DHT - Alone. It uses a sample from Heart - Alone. Now they are making a single from it but they had to re-sing it.
Another example is The Logical Song by Solid Solution. The original came from Supertramp. The vinyl has the original sample, the single edit has new vocals.
Here are the examples
DHT - Alone (vinyl)
Solid Solution - Logical Song (vinyl)
Solid Solution - Logical Song (single)