I want to install vinyl siding over my old siding which is soft in some places, probably rotten (I dont know how to determine, you can see attached photo). But I've heard that it's not a good idea to install a new over existed rotten. But what if I cover old siding with waterproofed home wrap before I install new vinyl? I think there will be no moisture anymore and I shouldn't have any problems. Is it a good idea?
Is it soft enough that your nails will pull out? If your nails won't hold, you need to replace soft sections with OSB or plywood. Since you're covering the wall, it won't need to be pretty.
Follow manufacturer instructions regarding vapor barriers.
Vinyl siding over the existing rotting siding is not a repair. A repair includes replacing rotten materials with new. Removing the rotted material without replacement might be an alternative if the siding is not part of the walls lateral resistance system (for example siding backed by structural sheathing).
There isn’t really any form of good construction that involves leaving rotting materials in place. Rot does self heal.
Now is the easiest time to fix it. Everything is accessible and less damaged than it will be in the future.
In addition, fixing it now will make installation of new siding easier and the installation more sound. You won’t be dealing with failing new siding due to rotten substrate. Often this type of repair turns out to be less work than peoples imagine...even when the issues are worse than what appears on the surface.