I'm going to save you some time if you don't feel like reading through the full list of waiver claims awarded to NFL teams yesterday, because it's pretty long. The San Diego Chargers didn't get any new players added to their roster.
Here's how it works: When a player is "cut", they are actually waived. Other teams can choose to claim that player, I believe the one with the worst record from the previous season wins the waiver claim, and assume his contract once they give him a roster spot.
Either the Chargers had some rotten luck with their waiver claims yesterday, or they didn't submit a single waiver claim. The latter would say that they are very happy with their 53-man roster and didn't see a single player released yesterday to be an improvement over even the last guy on their roster. That would be a pretty incredible claim.
It's probably more likely that they were selective with their waiver claims and just didn't see anything that the rest of the NFL, including teams that had worse records than them last year, didn't also see.