Sky King is right about how to ride through an intersection ... you're a vehicle just like any other.

As far as pedestrians - I've never seen a sign like that at an intersection where the other side didn't have pedestrian facilities. So you just cross at the other side.

Now, I know plenty of roads and city streets that have no pedestrian facilities at all, and I just yesterday had to deal with some construction like Eden is talking about. But they don't have signs forbidding pedestrians to cross at both sides. Where there are no pedestrian facilities at all is almost easier - you wear your scrubby jeans and your hiking boots and expect to walk in the ditches, climb the banks, etc., but when there *is* a sidewalk but it's closed, typically you have no choice but the road, which can be super busy with no shoulder.