I was recently terminated by the cleaning company I worked for. Now I'm working for an individual. Two or three current customers of the previous company that I worked for found out and now want to hire this individual so that I can continue to clean their homes. Can I do this and remain loyal to the non-compete agreement.

Doesn't sound like it. Its possible even working for another cleaner violates the agreement. However, if a non compete agreement prevents you from earning as living it could be voided.

But stealing customers from a previous employer would be a nono, even if they want to switch.