Besides over voltage protection, what other purposes are served by the shrink-wrapped (in yellow) components seen here? Do they have any effect on discharge, and will they discharge the battery other than parasitically in normal discharge use?
The protection circuits you find in these LiPos can also do over current protection, and under voltage protection so you don't take too much out of the cell and wreck it.
Protection circuits do draw a little bit of power, but it is microscopically small, like micro or nano amps. Designers make sure the cell is big enough, and the lower voltage threshold is high enough, that it would take an extremely long time for that parasitic current to take the cell below a safe threshold. It could years or decades, much longer than it would take for the battery to die of self-discharge.
Here's another great stack exchange post that goes into more detail: To protect a LiPO cell from undervoltage, how low current is low enough?