If there was an engine malfunction, could we breathe contaminated air?
Yes, an malfunction in a jet engine can cause contaminated air to reach the passenger cabin. It is a rare occurrence, but it does happen. 

One of the most famous cases was British Midland Flight 92 on Jan 8th 1989 in Kegworth England. 

Kegworth air disaster

"After taking off from Heathrow at 7:52 p.m., Flight BD 092 was climbing through 28,300 feet to reach its cruising altitude of 35,000 feet when a blade detached from the fan of the port (left) CFM International CFM56 engine. While the pilots did not know the source of the problem, a pounding noise was suddenly heard, accompanied by severe vibrations. In addition, smoke poured into the cabin through the ventilation system and a burning smell entered the plane".

In addition to contamination from engine failures, there is a much more public debate over contamination due to perceived weaknesses in the design of the aircraft cabin air systems. These weaknesses have not been positively identified but many believe it is due to faulty engine seals and/or air conditioning packs. There are numerous reports of pilots, flight attendants, and passengers feeling ill from "toxic air" on aircraft. 

The name "Aerotoxic Syndrome" is also used to describe the problem of bad air in aircraft. More information here: Aerotoxic syndrome

Here is a website dedicated to Toxic Cabin Air. Toxic Cabin Air