This is a very common trick used in many audio amplifiers with an op amp topology to minimise the output offset by creating a unity gain for DC. Usually the electrolytic capacitor sits on the ground so it operates around zero. The voltage drop is usually miniscule. Does it make a sense to provide an additional bias to the capacitor to increase its life span? It's believed that ±0.5V is a safe area but I can't find any concrete proofs.
The cathode of an aluminum electrolytic capacitor has a thin oxide layer (as opposed to the thick layer on the anode) that can withstand a few hundred mV (typically ~1V).
Applying excess reverse voltage continuously can result in reduced capacitance as the oxide layer grows, even if it doesn't cause excessive heating and venting of electrolyte. But <50mV or so isn't going to do anything.
Note that in your circuit if a low frequency AC voltage is applied, the capacitor can see some positive and negative voltage, up to approaching the supply voltages.
You could also use a nonpolar or bipolar electrolytic which has thick oxide on both anode and cathode. Or two ordinary electrolytics back-to-back. Or put a 1N4148 across the capacitor.
Applying a bias is possible (for example you could connect the capacitor to the negative rail rather than ground) but that sounds like a good way to inject noise into the amplifier circuit.
