Having the outputs actively set to High or Low only happens if the OE/ pin is low. http://www.ti.com/lit/ds/symlink/sn74hc595.pdf You cannot have some pins actively driven high and low and others disabled.
What could be done is to use a TPIC6C595, which has Open Drain outputs. A pullup resistor is added to each output to bring it to a high level. When a 1 is shifted in, the output is active and goes low. When a 0 is shifted in, the output is inactive and gets pulled high by the resistor, and other devices can then pull it low if needed.
If the question is "If a pattern (byte) is shifted in and the data does not change for some bits, do the unchanged bits stay the same at the output?" the answer is yes, the unchanged bits do not change. You can shift on 00001111 and then 10101111, the two upper bits will change from 0 to 1 while the 4 lower bits just stay at 1. The outputs get updated on the rising edge of the RCLK pin.