"Ne zaman kayboldu?"

Kaybetmek = to lose something
This is a transitive verb, and it will require accusative case on the object that has been lost.

• Anahtarlarımı kaybettim = I lost my keys
• Kedimizi kaybettik = We lost our cat
• Aklını kaybettin mi? = Have you lost your mind? ;-)

Kaybolmak = to be lost
This is an intransitive verb, and the lost item is now the subject, so it stays in nominative case:

• (Ben) Kayboldum = I got lost
• Kedimiz kayboldu = Our cat was lost
• Anahtarlar kayboldu = The keys were lost /vanished

(This is a good way to deflect responsibility: I didn't loose the keys... The keys got lost on their own, haha!)

I will check with some friends, but I do not think so. If you do that, you would be telling someone to literally get lost (and in to intentionally lose their way).