what would cause engine light to stay on in a 2014 Chevy malibu?

The red engine light means do not drive or even start the engine or damage will result. On a GM it’s usually a failed oil pump, but if you drove it that way then it can mean a new engine is needed.

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Any of hundreds of reasons will cause a CEL to illuminate, you have to scan for codes and then diagnose the problem.. That's what mechanics are for.

Visit your local auto parts store and have them scan the computer for trouble codes. Most stores will do it for free. Since the check engine light is on there's at least one code in the computer. Post the code here and we can help further. Jim

Clarify your question, is it a red engine light or a yellow check engine light.

if its red shut it off.if its yellow get it checked soon