"Thin" and "drop protective" are mutually exclusive. The thinner a case, the less protective it's going to be, at least until they come invent or discover some material with qualities that will defy current laws of physics.
Those sliders suggested above are slim but won't do much to protect your phone if you drop it just right. They do little to dissipate shock.
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You might try the Element Case Ion 4. I absolutely LOVE this case. It adds minimal bulk and does provide some excellent corner shock absorption. This is possibly my favorite case (and I own 25+ cases, and counting, with more coming).