Bright, there are a few restoration services that work to restore hard drives by moving the platters to a custom reader and these could be able to pull data off simply because of the sector offsets. However were talking huge money, these services are prices for things like "oh the company laptop with irriplaceable data was dropped / in a fire / car crash and we need this data!
That said if you are looking to keep data from the police, they use similar hardware and will probably make short work with a single pass zero (although I imagin it is not a %100 restore). In cases like these.. just trash the drive.
Are you kidding? No such software exists. Writing zeros to the drive actually physically changes the charge on the gate or the magnetized portion of the platter. Unless the data is stored elsewhere on the disk (such as a remapped sector where the original was marked bad) the data is not recoverable. There are several BIG prizes out there for recovery software companies that can recover one file from a disk that had zeros written to it and no one has done it yet.
A decade ago, with very advanced technology and a boatload of money, recovering a bit or 2 may have been possible. Each track on a disk had a gap between it and the next track since the magnetic field of the read/write head didn't jut cut off instantly. That gap was theoretically within the size limits of a electron microscope, so the magnetic bleed over could theoretically be read in some instances, though no researcher, company, or organization has ever successfully done so and been proven.
However, that hasn't been how hard drives have been laid out for years. Now, a bit it is an estimate because the tracks are so close together that a read pass will read more than 1 track width, especially while the head is settling into the new track. It is more similar to "well, this bit is most likely 1; that bit is probably a 0; the checksum matches, so let's pretend they are." and that is what gets returned.
On an SSD, I don't know of any tricks that could be used once the data is changed besides the same possibility on magnetic media; which is read data out of the spare area or similar.