I don't think I can explain the science behind it, but Echoes are strange things.

Sometimes, they're fuzzy memories. Others, they're stuff your past life owned. [He holds up his hand, displaying a rather prominent ring on his finger. It's silver, with a huge lapis lazuli inset gem along with his [past life's] family crest in silver. If Misa looks closely, it'll have his initials - SS.] Some even get family pets.

If you ask me, I think it's luck of the draw.