In almost all situations you could. The exceptions would be:1) You had signed a non-compete with the owner him/herself (e.g. not with the defunct business) and the owner him/herself is still in that line of work, just not with the previous busienss--in that case, the noncompete might still be enforceable.2) You are using assets that are not yours to start the business, including the client or customer list of the former business--whether or not that business is still in business, it's assets are not yours and you could not use them.3) You are advertising yourself as being the successor to or continuation of the old business, when you're not--though you can truthfully say you worked at the former business.Other than the above, you should be able to.