Law enforcement may conduct a warrantless search if they are pursuing a fleeing individual, there is an ongoing emergency, or other exigent circumstances such as destruction of evidence.  However, law enforcement may not create the situation that caused the emergency.
U.S. Supreme Court
This Court has identified several exigencies that may justify a warrantless search of a home. See Brigham City, 547 U.S., at 403, 126 S.Ct. 1943. Under the ‘emergency aid’ exception, for example, ‘officers may enter a home without a warrant to render emergency assistance to an injured occupant or to protect an occupant from imminent injury.’ Ibid.; see also, e.g., Fisher, supra, at ––––, 130 S.Ct. at 548 (upholding warrantless home entry based on emergency aid exception). Police officers may enter premises without a warrant when they are in hot pursuit of a fleeing suspect. See United States v. Santana, 427 U.S. 38, 42–43, 96 S.Ct. 2406, 49 L.Ed.2d 300 (1976). And—what is relevant here—the need ‘to prevent the imminent destruction of evidence’ has long been recognized as a sufficient justification for a warrantless search. Kentucky v. King, 563 U.S. 452, 460 (2011)
Over the years, lower courts have developed an exception to the exigent circumstances rule, the so-called ‘police-created exigency’ doctrine. Under this doctrine, police may not rely on the need to prevent destruction of evidence when that exigency was ‘created’ or ‘manufactured’ by the conduct of the police. See, e.g., United States v. Chambers, 395 F.3d 563, 566 (C.A.6 2005) (‘[F]or a warrantless search to stand, law enforcement officers must be responding to an unanticipated exigency rather than simply creating the exigency for themselves’); United States v. Gould, 364 F.3d 578, 590 (C.A.5 2004) (en banc) (‘[A]lthough exigent circumstances may justify a warrantless probable cause entry into the home, they will not do so if the exigent circumstances were manufactured by the agents[.]’ Kentucky v. King, 563 U.S. 452, 461 (2011)