In no case in which sufficient amount of people oppose something, a policy can pass. Of course, Im talking about proportional representation systems. In first past the post, what you speak of is possible if that issue is not so critical to that amount of people that they may not vote on it as their #1 issue. Then the opposing party can win with a low margin on some other issue in which they have majority, meanwhile passing that other policy as well. This is an ill of the FPTP system. In proportional representation, that does not happen.

Of course, FPTP itself is something that was implemented to avoid the democracy of the majority, so that's no surprise.

With a single-subject rule, that’s often (but not always) true; without it, it is less true, because policies can be packaged to achieve a combined majority, so long as there isn’t a majority that thinks it is important enough to defeat any part to overcome any support within that majority for other parts. (Even with a single-subject rule, this can sometimes be done, so long as the policies packaged relate to sufficiently closely related subject matter as to fit within the way the rule is applied.)

This is common in legislative bodies, and it works with citizen-legislators, too.