My question is this: what does an input see when connected to a Hi-Z output?
An almost perfect open circuit.
U1 is called a "tri-state" device. Each output pin has three defined conditions: logical high, logical low, and a very high impedance that cannot be relied on to either source or sink current. In the device output stage, both the pull-up and pull-down transistors are off.
Note that the 374 output leakage current is specified as "+/-". This means that for a "typical" part, the output current can be anything between +5 and -5 uA. This is a clear indication that any inputs connected to these outputs must be terminated through a less-than-infinite impedance path to a defined voltage level that complies with the input voltage specifications
If you want a downstream device to see a particular bit pattern when the 374 is in the tri-state condition, you can add high-value pull-up and pull-down resistors to the data path. For example, 10K to 100K resistors are small enough to be overpowered (safely) by the 374 output stage when active, and provide stable input termination when the 374 is in tri-state.
Gold star for providing datasheet links without prompting.
Clarity: If the B inputs all are at 0 and the A inputs are floating (due to the 374 tri-state condition), the S outputs will be a random number. Due to input stage capacitance, there will be a time period during which the A inputs will "see" the last valid states from the 374 before those outputs went tri-state, but the capacitances are so small and the input impedances are so high that someone walking past the circuit will affect the input states.
[Added from comment on other answer] Unlike a TTL input stage, a CMOS input stage has no implicit bias toward either logic state. If a CMOS input ls left floating, the potential at the input pin will be somewhere between Vdd and GND. If it drifts to something around 50% of Vdd, it is possible for both pull-up and pull-down transistors in internal stages to come partially on at the same time, creating a relatively high current path from Vdd to GND. This current can be high enough to cause device failure.