It's a good prompt, because it encourages thinking about how the fields work.
They aren't just some free-willed inscrutable thing, after all. The fields depend upon motion of charges, and boundary conditions. Which is to say, more motion of charges, but we can treat shields, dielectrics, etc. as boundaries to media with characteristic properties, no need to do a full particle simulation every time you throw the light switch and all.
Say you have a near-plane wave propagating along the wire. (I suppose it won't be a perfect plane wave, as it's dragged inward a little bit by the wire.) The wire ducks into a hole in a metal sheet. Currents flowing on the wire, reflect image currents in the sheet, and so the field effectively scrunches down as the wire approaches the sheet. If we're talking high frequencies, most of the energy reflects off the plane, and yes, it effectively blocks radiation -- the wire has a fairly small cross-section (locally it acts like a whip antenna, albeit of somewhat indeterminate length since, well, it's long -- particularly if we're assuming an infinite wire passing though a small (not touching) hole in a perpendicular sheet of infinite size). Some remainder couples through, is re-radiated in the same way on the other side, and there you are.
Well, inside and near the hole: you have current on the wire all the way through, some potential with respect to ground, and thus some electric field. Outside the hole, the field will be fairly mild (making roughly 1/4-circular arcs from wire to plane, up in the near field of course i.e. we can locally ignore wave propagation), rising in intensity as you approach the edge of the hole (the arcs get shorter and shorter). Inside the hole, the E-field lines are largely radial, approximating a coaxial cylinder structure. Likewise the currents are largely radial outside the hole (converging on it like a black hole), then longitudinal inside.
The field is, and isn't, blocked. For sure, there's no abrupt brick-wall stoppage, it's not like it's a...cloud of tennis balls or something.
Specifically, we can consider the superposition of free propagating (and subsequently reflected), and wire-guided (and subsequently transmitted), waves, and realize that one is blocked, the other not. There is some coupling (the wire picks up some propagating field on both sides) so it's not completely independent, and, I'm not entirely sure how you'd set up a problem around an infinite wire (if it's resistive, it'll drag down all the field around it, until nothing's left -- depending on which axis you consider "infinite-er"); maybe you still need the excitation source at some finite distance, so you're really modeling waves inside a large box, rather than infinite space. And then you get standing waves, severity depending on how the other boundaries are modeled (an impedance-matched source wall would be good to keep the bandwidth stable). Anyway, it'll be something -- boot up the simulator yourself, I'm sure I've missed something here.
Tim