I believe they definitely do for a time. My lover and myself have both experienced this directly. However, I also think after a time that they pass on. Perhaps they leave a piece of themselves with us though? I'm not entirely sure how it works after the 'passing on' period. I suppose it would depend (according to my philosophy) on which of the routes they took after passing and when they entered that route. I'm pretty sure that for most there is a 'grace period' of weeks to months to even a couple years, though.