Off the top of my head, two come to mind. Newhall, and the Miami Platt/Mattix shootout. Not saying the shotgun is a bad choice. But its not magical, and people can and often do miss with buckshot. The two incidents listed below are anomalies. But they show shotguns can run dry with no effect, and they were not reloaded although they needed to. Both instances the officer transitioned to a handgun. Most likely they had no rounds available to reload.
Given a choice (and our agency has that choice) of one long gun per agent (14" 870, 11.5" or 14.5" M4s, very limited number of MP5A3s) I have the M4... Shit gets knocked, bumped, smacked etc, and I trust the M4 safety far more than the shotgun's. I also get more rounds, lower recoil, easier reloads, etc... BUT, when the only option we had was 870s, I never felt unsafe or outgunned. I have seen several people killed with shotguns (crime scenes). They were pretty chewed up.
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NEWHALL: Meanwhile, Officer Alleyn emptied his Remington Model 870 shotgun at the Pontiac, firing the gun so fast he accidentally ejected a live round in the process. A single pellet from the shotgun struck Twinning in the forehead, but it did not penetrate his skull and only inflicted a minor superficial wound. After expending all his shotgun rounds, Officer Alleyn opened fire on Davis with his .357 Magnum revolver, but did not make any hits. Davis returned fire with his sawed-off shotgun, striking Alleyn with several rounds of 00 buckshot and inflicting fatal injuries.[4][7]
PLATT/MATIX: Agent Mireles fired four more rounds from his Remington 870 at Platt and Matix, but hit neither.[18]