The concept behind using a live for cd distro is quite simple in nature. When you can't read from a drive as well as not being able to boot up with it but the drive can still be read from having working read/write heads the OS is loaded totally independent from a cd-r.
Even if both of the drives seen in the image were lacking boot information you can still see right onto both without problem. The same could be done with one drive being a usb model with the boot information corrupted on the other host drive and refusing to boot up.
If the heads on the OS drive are still good you can still copy files from that onto another one even if the host is seeing bad sectors. You simply won't be able to rescue anything where the bad sectors are present.
As far as the bootstrap also a rather old term and how the bios plays a role once the OS has created an mbr that gets into a little more detail.
BIOS role in bootstrap
- The BIOS loads sector zero (CHS=0:0:1) of the boot drive to linear address 7C00h
- The BIOS checks the loaded sector for the magic bootstrap signature bytes: 55h at offset 510 and 0AAh at offset 511. Many BIOSes will load and execute sector zero, regardless of the value of these bytes. MBRs, however, will check for the presence of these bytes.
- CPU register DL is set to the boot drive number: 0 for floppy drive A, or 80h for hard drive C.
- BIOS jumps to sector 0 code it just loaded.
Further details like the mbr's role in the bootstrap can be looked over at
http://my.execpc.com/~geezer/osd/boot/index.htm