As a human, death is inevitable, even for healthiest person in the world (ageing cannot be stopped). When a normal human die, their soul chain is cut. However, things are different those with unactivated shinigami power who obtain shinigami power while they are still alive through unnatural means, like Ichigo. The question that many of us has been wondering is that what would happen if human with in-born Shinigami power (activated), die while they are in human form.
closed as primarily opinion-based by Makoto, 絢瀬絵里, pap, Michael McQuade, Alagaros Jun 24 '16 at 9:31
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
If we go with other people who died in Bleach, the moment they died, their soul came out of their body. Unlike people who only half-dead, like Inoue when she was assaulted by his brother who has turned into a hollow, a dead people have his chain of fate separated from his body, which means he won't be able to return to his body. His body would still have the chain and if let on his own, the chain would start to erode until when it eroded completely, he turned into a hollow.
Shinigami is a soul, as can be seen during the flashback of Rukia and Renji's past. Both was resident of Rukongai, the residential district. And it was shown during Chad's awakening that a soul that is sent to Soul Society is sent to the Rukongai area. This suggests that Rukia and Renji was a human too before they starts entering the Shinigami academy and turned into one.
Now, since Ichigo is already a Shinigami, and a Shinigami is a soul, then if he died he would just simply turned into a Shinigami, except that he won't be able to return to his body. He can of course enter a gigai shaped just like his body.