Is there any linux distro that can write to media to which it is installed
 

I need an os. that boots up and when I shut down it should write the changes to the media from which it is running.

as long as the medium isn't read-only by nature (optical drives for instance), then any distribution, installed properly can do this.

Every installed OS weather it is Linux , Microsoft , or Apple dose this as part of the NORMAL operating procedure

it IS HOW as computer OS works

It sounds as if you are talking about booting to removable media, rather than a hard disk.

This link should help if I guessed correctly: http://linuxathena.com/tutorials/boo...ve-unetbootin/

When a system boots, say, using the GRUB boot-loader, then the majority of the boot-time software (including most of GRUB itself) is located in "an ordinary directory on the hard drive." The kernel is also found there, and the boot-loader knows how to navigate the file-system to find it. Although it is customary best-practice to make those files (and often, the entire /boot branch) read-only, those areas can still be writable. Furthermore, although it is frequently the case that areas such as /usr may correspond to other partitions on a multi-partitioned media ... again, there is no physical requirement for this to be so.

You could easily organize your boot-media so that it contains the customary-and-protected boot-folder and, on the very same media, other read/write areas of the file system to which any application may read or write at any time.

When you "shut down the system," what actually happens is that the system switches to a different "run level." (See man inittab e.g.) When this happens, init/systemd begins to execute a prescribed series of programs, the cumulative effect is to shut the system down in an organized fashion. (There's a lot of detail here that I won't go into now ...) But, if you want particular things to be-sure-to happen as you shut the machine down, this is the place and the method by which to do it. On any Unix/Linux system. You can precisely determine what happens and in what sequence it happens.

Look at: man service.

Frankbell,yes I wanted to know if I could save to removable media like rewritable CD-ROM

flash drives, yes, but unfortunately rewritable cd-rom isn't random access, it has to be erased before re-writing, so i highly doubt that would be practical (theoretically possible yes, but horribly impractical)

Well, what about a multi-session DVD ? That might work, but it doesn't make much sense to do so. I mean it wouldn't work like you think it would. You would have to append a session with some files, but it wouldn't change the first session.