The short answer is yes. There are inexpensive or relatively cheap franchises available in the market places that have a proven track record of being profitable and making money for its owners. Most of these franchise concepts tend to be home based, have no inventory, and provide some type of service to consumers and small businesses.
How do you confirm if a concept has a biz model that has a track record of being profitable? The best way in my opinion is to contact franchise opportunities that meet your investment and personal requirements and ask if they provide earning statements in the their FDD or franchise disclosure statement. Or better yet as part of your due diligence ask the franchiser to provide you several names and phone numbers of existing franchisees and ask them to validate they are making an actual net profit after all expenses.
You can research some inexpensive and low cost franchises here.