I haven't used one myself, although I'm thinking about it... The FAQ page on the mooncup website has some suggestions on how to prevent leakages, although it doesn't specifically talk about leakages at night.
http://www.mooncup.co.uk/menstrual_cup_faq.htm l#Leakage
I hope it helps.
From a logical point of view aren't leakages more likely at night just because when you're lying down the cup is no longer upright? This isn't mentioned on the website as far as I can see and is just me pondering so might be a load of rubbish, also it doesn't really answer your question or help in any way
;o|