I have connected big capacitors to the speakers to increase the bass. Now, after months of using, I notice that one of the speakers sounds 2x low. I ejected those big capacitors, still the same. I don't know how to test the caps. So I'm asking theoretically, could those big caps have damaged the small ones?
Unlikely, but yes.
A capacitor and the coil of the speaker form an oscillator, which will resonate to some frequencies more than at others. Resonance means you get larger voltages.
Adding resonance to a system can hence introduce voltages that you didn't design for. That can, in turn, break voltage-sensitive components such as capacitors.
Why it's unlikely: The smaller capacitor you used is probably sufficiently robust against overvoltage; also, speaker capacitors tend to be of the self-healing film type, so only a reduction in capacity would be noticable, with should shift the frequency response, but not lead to a reduction in output power with a sensible test signal (I assume that's what you mean with "2x low", whatever that exactly means).
More likely are cabling problems or a damaged speaker.