There is no "block", only "attenuation" or reduction of signal. So even something that may seem impenetrable to radio signals is not, it only reduces a certain amount.
Radio signal in the real world tend to be measured on logarithmic scales, because of the massive range of signal strengths that are encountered and useful.
Consider the following:
Cutting a signal level in half, in logarithmic terms, is a 3dB reduction. Cutting it in half again (so now 1/4 of the original signal) would be 6dB.
The signal meter on a typical amateur radio transceiver, from strongest to weakest signal, covers roughly 100dB.
A basic duplex repeater in two-way radio has a filtering system to isolate the transmitter and receiver from each other, which typically have an isolation of 80 to 100dB.
So even what seems like a good shield, and even if it is a good shield, may still not be enough to prevent a device from being able to communicate through that level of attenuation. To accomplish that amount of attenuation would take a lot of attention to detail. Without sophisticated equipment the best bet would be to use multiple layers, as the attenuation of each layer is additive to other layers. Actually the best bet would just be to remove power from the device so it can't function.