I bought Polk LS50 from craigslist for my kids. One speaker produces some static noise and it sounds much weaker than the other.
It wouldn't hurt to open it up and check the wiring. If it's a loose (or bad/ pitted) connection then that should be easy enough to remedy.
It wouldn't hurt to have a quick look.
It might just be connection wire that's come loose in transit.
If you haven't opened up a speaker before it can be quite daunting.
Nevertheless, with a bit of care and a good torch you should be able to check the obvious. It might be a good idea to use tape to mark the driver position before removal and also try to replace the wood screws into the same holes (same tightness) they were in originally.
Perhaps take a picture too to remind yourself later and avoid checking again.
If it's not that, then why not give Polk a ring?
If anyone's familiar with that issue then it will be them.
The real nightmare is if someone has futzed with the crossovers.
That's always a worry buying used.