if you watch the the great shredders the fingers that are not being used to fret a note are very close to the strings

how would you work on getting your unfreted finger closer to the strings?
by leaving them on the string but not touching them too hard, very lightly. not really hard
I think it has a lot to do a lot of the best guitar players hands being so big that their fingers just tend to look like they are wrapped around the entire guitar and so close to the strings...There are are guitar players that don't neccesarily do this, Trey Anastasio comes to mind and he rips...I wouldn't worry to much about trying to practice doing this...Practice getting better at playing the guitar and it shouldn't matter how far or close your fingers are to thr strings as long as you're hitting the notes. I've thought about this too before and kinda came up with this since I don't hae huge hands and people like Jimi, and SRV did.
when shredding, u often need to mute string u r not picking so that they dont produce any unwanted noise, and this muting can be done by slightly touching the strings with fingers u r not using to fret any strings. By practice it becomes second nature.