If my husband has been diagnosed with cancer and the doctor believe that it is from his previous job, can we sue the company?

You may be able to sue the company. First, you'd need to be starting or initiating the suit within the "statute of limitations," or time period to sue. The statue of limitations, or SOL, is normally 2 years for personal injury or illness in your state that means suing within 2 years of the last exposure to the hazardous chemicals or conditions. This time period can be tolled, or extended, if you were not and reasonably would not have been aware of the harm or injury, so if your husband only discovered the cancer within the last 2 years, he may still be able to sue.
Second, you have to have good evidence of causality so medical experts and medical literature e.g. published studies or reports showing a link between the specific chemicals to which your husband was exposed and his type of cancer. You can't just allege that there was "smoke and chemicals," but have to show what those chemicals were and their link the cancer.
Third, you'd also have to show that the employer did not take reasonable safety precautions, at least in light of what was known at that time if they did take all then-reasonable precautions, they may not be liable.
Finally, bear in mind that if the employer went out of business or was sold to a different person or entity since your husband worked there, it's possible that there is no one to hold liable. It depends on the specific facts of their going out of business or the sale, but this is risk if there was been any change in ownership or operatonal status.
It would certainly be worth your while to discuss the matter in detail with a personal injury attorney. Many provide a free initial consultation to evaluate cases, and you can ask about this before making the appointment.