What happens to a person's pensive after they're gone?

[woman22980]

No: HPFGUIDX 143659

Hey all!  I was wondering if anyone could point me to some theories as 
to what happens to a person's pensieve after their dead?  What happens 
to Dumbledore's pensieve?  Will Harry inherit it?  Perhaps with DD's 
pensieve he can finally learn why DD trusted Snape so unequivocally.  
He could learn tons more than that, depending on what was put in 
there, but that's something I think Snape isn't going to be really 
forthcoming with Harry about (in between blasts from wands and all.)

Also, now that Snape's run out of the castle, does anyone think he 
left behind _his_ pensieve with anything in it?  I'd love to see more 
of Snape's memories, maybe he did fall in love with Lily, and that's 
why LV gave her a chance to live - to reward Snape for his great 
service of delivering the prophecy. (ancillary to the question about 
Snape's pensieve, but that's the second mystery I'm dying to know more 
about.)

It's probably been discussed before - I think evertying has been 
discussed on this list!  but that's the thoughts that are keeping me 
up late this night.  Does anyone know if JKR has mentioned something 
about DD's pensieve?

Jenny