Encroachment

During Ichigo's training, he went through a particularly lethal lesson called Shattered Shaft. He had to escape the shaft in time to gain his own Soul Reaper Powers, or else he'd become a hollow.

Pluses
The Encroachment is when a plus begins the process of transforming into a hollow. Once the chain of fate is separated from a spirit they can no longer return to their physical body. Death for the soul comes within 72 hours, once the chain is completely eroded. One symptom right before the last erosion is an increase in appetite, as stated by Jinta. The last erosion is nothing like the others, as Ichigo still had seven links of his chain, as opposed to the one link per erosion before it. They become hollows afterward, and have no chance of returning to their spirit form -the transformation is permanent. When a Plus descends into a hollow his/her spirit form shatters and reconstitutes into a different form. Then their Hollow Mask manifests.

Resistance
Urahara replied when Ichigo asked if he was trying to kill him, "Yes....the moment you give up," implying the Encroachment can only be overcome by those who have the will to do so. While the standard plus usually becomes a hollow straight away, Ichigo Kurosaki was able to fight it if only long enough to defeat it. The transformation went completely out of sequence: His mask was being born first while his body was still a plus. The white substance forming the mask was almost pouring out of his eyes and mouth and began to cover the right side of his face. Had the process continued it would have completely formed with no chance of returning to a plus.

This ability to resist may or may not be implied for all souls, just those similar to Ichigo(see below.)

People with Latent Shinigami Abilities/High Spiritual Power
The real test wasn't to escape the shaft, but for Ichigo to become a shinigami while simultaneously preventing his own hollowfication- if a soul were to reach the encroachment and gain shinigami powers in time, they can prevent their death. Fortunately enough Ichigo found the strength to resist the transformation and find his own Soul Slayer, Zangetsu, just in time.

Ichigo was born from a human mother(Masaki Kurosaki) and a shinigami father (Isshin Kurosaki), so he was born with the potential to become a shinigami. However his true heritage was not revealed until the Arrancer Arc, so it can be assumed Kisuke's method of forced Encroachment along with the natural version could cause any soul with sufficient spiritual power to gain shinigami powers and or turn into a powerful hollow.