Question bomb from a semi-noob

Silence only limits the ability to use active skills, the exceptions are Doombringer and Disruptor's ults which both limit active skills, most passive skills, and all activatable items.

A lack of mana won't stop a passive because a passive is a no-cost always active ability (unless disabled by Disruptor or Doombringer), I think what you meant by passive is auto-cast abilities such as ability modifiers like Viper's Poison Attack. These auto-cast abilities are treated as active skills (because they can be manually casted and toggle the ability of being auto-casted on or off), and any thing with a cost will obviously be unusable if you lack the ability to pay the cost. In this case Viper's 20 mana cost for Poison Attack, if you have 19 mana then you can't use it. But if a passive ability is in question then the lack of mana has nothing to do with it as previously stated due to the lack of a cost.

They don't stop Passives in general, but Permanent Invisibility is the only exception I can think of.