The devil's palm is a deadly place, a mysterious and drought desert constantly shifting its surface, making surviving after entering extremely difficult, however, those who do survive (presumably those who have sufficient spiritual strength, like the ones that were chosen by the arrows), may be granted a stand ability. e.g. Mountain Tim or the Boom Boom family.
The saint's corpse parts also grant stand abilities, for those who fused with a certain part of the corpse may gain a stand under the corpse's holy power, however this does won't happen for certain (Gyro didn't gain a stand but instead had the ability to see stands) e.g. Johnny Joestar and Funny Valentine.
In some cases, the stand ability granted will disappear once the corpse part is severed from the person. Presumably, this is because the corpse's holy properties bless the person who fused with them, thus giving people who originally couldn't awaken a stand the opportunity to have one, so once the corse part is severed, the blessing ends and the stand disappears. Johnny's stand ability is granted and dependent on the corpse part in the beginning, but after his spiritual strength grew and he matured, his stand stayed with him and no longer needed the aegis of the corpse part to exist.